Robot Having Arm With Unequal Link Lengths

ABSTRACT

A transport apparatus including a drive; a first arm connected to the drive, where the first arm includes a first link, a second link and an end effector connected in series with the drive, where the first link and the second link have different effective lengths; and a system for limiting rotation of the end effector relative to the second link to provide substantially only straight movement of the end effector relative to the drive when the first arm is extended or retracted.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of copending application Ser. No.13/833,732 filed Mar. 15, 2013, which claims priority under 35 USC119(e) on U.S. Provisional Patent Application No. 61/754,125 filed Jan.18, 2013 and U.S. Provisional Patent Application No. 61/762,063 filedFeb. 7, 2013 which are hereby incorporated by reference in theirentireties.

BACKGROUND Technical Field

The disclosed embodiment relates to a robot having an arm with unequallink lengths and more particularly to a robot having one or more armswith unequal link lengths, each supporting one or more substrates.

BRIEF DESCRIPTION OF PRIOR DEVELOPMENTS

Vacuum, atmospheric and controlled environment processing forapplications such as associated with manufacturing of semiconductor,LED, Solar, MEMS or other devices utilize robotics and other forms ofautomation to transport substrates and carriers associated withsubstrates to and from storage locations, processing locations or otherlocations. Such transport of substrates may be moving individualsubstrates, groups of substrates with single arms transporting one ormore substrates or with multiple arms, each transporting one or moresubstrate. Much of the manufacturing, for example, as associated withsemiconductor manufacturing is done in a clean or vacuum environmentwhere footprint and volume are at a premium. Further, much of theautomated transport is conducted where minimization of transport timesresults in reduction of cycle time and increased throughput andutilization of the associated equipment. Accordingly, there is a desireto provide substrate transport automation that requires minimumfootprint and workspace volume for a given range of transportapplications with minimized transport times.

SUMMARY

The following summary is merely intended to be exemplary. The summary isnot intended to limit the claims.

In accordance with one aspect of the exemplary embodiment, a transportapparatus has a drive; a first arm connected to the drive, where thefirst arm comprises a first link, a second link and an end effectorconnected in series with the drive, where the first link and the secondlink have different effective lengths; and a system for limitingrotation of the end effector relative to the second link to providesubstantially only straight movement of the end effector relative to thedrive when the first arm is extended or retracted.

In accordance with another aspect of the exemplary embodiment, a methodis provided comprising: rotating a first link of an arm by a drive;rotating a second link of the arm when the first link is rotated, wherethe second link is rotated on the first link; and rotating an endeffector on the second link, where the first and second links havedifferent effective lengths, and where rotation of the end effector onthe second link is constrained such that, when the arm is extended orretracted, the end effector is limited to substantially only straightmovement relative to the drive.

In accordance with another aspect of the exemplary embodiment, atransport apparatus is provided having a drive; and an arm connected tothe drive, where the arm comprises a first link connected to the driveat a first joint, a second link connected to the first link at a secondjoint, and an end effector connected to the second link at a thirdjoint, where the first link comprises a first length between the firstand second joints which is different from a second length of the secondlink between the second and third joints, where movement of the endeffector at the third joint is constrained to track in a substantiallystraight radial line relative to the center of rotation of the driveduring extending and retracting of the arm.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and other features are explained in the followingdescription, taken in connection with the accompanying drawings,wherein:

FIG. 1A is a top view of a transport apparatus;

FIG. 1B is a side view of a transport apparatus;

FIG. 2A is a top partial schematic view of a transport apparatus;

FIG. 2B is a side section partial schematic view of a transportapparatus;

FIG. 3A is a top view of a transport apparatus;

FIG. 3B is a top view of a transport apparatus;

FIG. 3C is a top view of a transport apparatus;

FIG. 4 is a graphical plot;

FIG. 5A is a top view of a transport apparatus;

FIG. 5B is a side view of a transport apparatus;

FIG. 6A is a top partial schematic view of a transport apparatus;

FIG. 6B is a side section partial schematic view of a transportapparatus;

FIG. 7A is a top view of a transport apparatus;

FIG. 7B is a top view of a transport apparatus;

FIG. 7C is a top view of a transport apparatus;

FIG. 8 is a graphical plot;

FIG. 9 is a side section partial schematic view of a transportapparatus;

FIG. 10A is a top view of a transport apparatus;

FIG. 10B is a side view of a transport apparatus;

FIG. 11A is a top view of a transport apparatus;

FIG. 11B is a side view of a transport apparatus;

FIG. 12 is a side section partial schematic view of a transportapparatus;

FIG. 13 is a side section partial schematic view of a transportapparatus;

FIG. 14A is a top view of a transport apparatus;

FIG. 14B is a top view of a transport apparatus;

FIG. 14C is a top view of a transport apparatus;

FIG. 15A is a top view of a transport apparatus;

FIG. 15B is a side view of a transport apparatus;

FIG. 16A is a top view of a transport apparatus;

FIG. 16B is a side view of a transport apparatus;

FIG. 17A is a top view of a transport apparatus;

FIG. 17B is a side view of a transport apparatus;

FIG. 18 is a side section partial schematic view of a transportapparatus;

FIG. 19 is a side section partial schematic view of a transportapparatus;

FIG. 20A is a top view of a transport apparatus;

FIG. 20B is a top view of a transport apparatus;

FIG. 20C is a top view of a transport apparatus;

FIG. 21A is a top view of a transport apparatus;

FIG. 21B is a side view of a transport apparatus;

FIG. 22A is a top view of a transport apparatus;

FIG. 22B is a side view of a transport apparatus;

FIG. 23 is a side section partial schematic view of a transportapparatus;

FIG. 24A is a top view of a transport apparatus;

FIG. 24B is a top view of a transport apparatus;

FIG. 24C is a top view of a transport apparatus;

FIG. 25A is a top view of a transport apparatus;

FIG. 25B is a side view of a transport apparatus;

FIG. 26A is a top view of a transport apparatus;

FIG. 26B is a top view of a transport apparatus;

FIG. 26C is a top view of a transport apparatus;

FIG. 27A is a top view of a transport apparatus;

FIG. 27B is a side view of a transport apparatus;

FIG. 28A is a top view of a transport apparatus;

FIG. 28B is a side view of a transport apparatus;

FIG. 29A is a top view of a transport apparatus;

FIG. 29B is a top view of a transport apparatus;

FIG. 29C is a top view of a transport apparatus;

FIG. 30A is a top view of a transport apparatus;

FIG. 30B is a side view of a transport apparatus;

FIG. 31A is a top view of a transport apparatus;

FIG. 31B is a side view of a transport apparatus;

FIG. 32A is a top view of a transport apparatus;

FIG. 32B is a top view of a transport apparatus;

FIG. 32C is a top view of a transport apparatus;

FIG. 32D is a top view of a transport apparatus;

FIG. 33A is a top view of a transport apparatus;

FIG. 33B is a side view of a transport apparatus;

FIG. 34A is a top view of a transport apparatus;

FIG. 34B is a top view of a transport apparatus;

FIG. 34C is a top view of a transport apparatus;

FIG. 35A is a top view of a transport apparatus;

FIG. 35B is a side view of a transport apparatus;

FIG. 36 is a top view of a transport apparatus;

FIG. 37A is a top view of a transport apparatus;

FIG. 37B is a side view of a transport apparatus;

FIG. 38A is a top view of a transport apparatus;

FIG. 38B is a side view of a transport apparatus;

FIG. 39 is a top view of a transport apparatus;

FIG. 40A is a top view of a transport apparatus;

FIG. 40B is a side view of a transport apparatus;

FIG. 41 is a top view of a transport apparatus;

FIG. 42 is a top view of a transport apparatus;

FIG. 43A is a top view of a transport apparatus;

FIG. 43B is a side view of a transport apparatus;

FIG. 44 is a top view of a transport apparatus;

FIG. 45 is a top view of a transport apparatus;

FIG. 46A is a top view of a transport apparatus;

FIG. 46B is a side view of a transport apparatus;

FIG. 47A is a top view of a transport apparatus;

FIG. 47B is a side view of a transport apparatus;

FIG. 48 is a top view of a transport apparatus;

FIG. 49 is a top view of a transport apparatus;

FIG. 50A is a top view of a transport apparatus;

FIG. 50B is a side view of a transport apparatus;

FIG. 51 is a top view of a transport apparatus;

FIG. 52A is a top view of a transport apparatus;

FIG. 52B is a side view of a transport apparatus;

FIG. 53 is a top view of a transport apparatus;

FIG. 54A is a top view of a transport apparatus;

FIG. 54B is a side view of a transport apparatus;

FIG. 55A is a top view of a transport apparatus;

FIG. 55B is a top view of a transport apparatus;

FIG. 55C is a top view of a transport apparatus;

FIG. 56A is a top view of a transport apparatus;

FIG. 56B is a side view of a transport apparatus;

FIG. 57A is a top view of a transport apparatus;

FIG. 57B is a top view of a transport apparatus;

FIG. 57C is a top view of a transport apparatus;

FIG. 58A is a top view of a transport apparatus;

FIG. 58B is a side view of a transport apparatus;

FIG. 59A is a top view of a transport apparatus;

FIG. 59B is a top view of a transport apparatus;

FIG. 59C is a top view of a transport apparatus;

FIG. 60A is a top view of a transport apparatus;

FIG. 60B is a side view of a transport apparatus;

FIG. 61A is a top view of a transport apparatus;

FIG. 61B is a top view of a transport apparatus;

FIG. 61C is a top view of a transport apparatus;

FIG. 62 is a top view of a transport apparatus;

FIG. 63 is a diagram illustrating exemplary pulleys;

FIG. 64 is a top view of a transport apparatus; and

FIG. 65 is a copy view of a transport apparatus.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENT

Aside from the embodiment disclosed below, the disclosed embodiment iscapable of other embodiments and of being practiced or being carried outin various ways. Thus, it is to be understood that the disclosedembodiment is not limited in its application to the details ofconstruction and the arrangements of components set forth in thefollowing description or illustrated in the drawings. If only oneembodiment is described herein, the claims hereof are not to be limitedto that embodiment. Moreover, the claims hereof are not to be readrestrictively unless there is clear and convincing evidence manifestinga certain exclusion, restriction, or disclaimer.

Referring now to FIGS. 1A and 1B, there is shown top and side viewsrespectively of robot 10 having drive 12 and arm 14. Arm 14 is shown ina retracted position. Arm 14 has upper arm or first link 16 rotateableabout a central axis of rotation 18 of drive 12. Arm 14 further hasforearm or second link 20 rotatable about an elbow axis of rotation 22.Arm 14 further has end effector or third link 24 rotatable about a wristaxis of rotation 26. End effector 24 supports substrate 28. As will bedescribed, arm 14 is configured to cooperate with drive 12 such thatsubstrate 28 is transported along a radial path 30 that may coincidewith (as seen in FIG. 1A) or a path, for example, path 34, 36 orotherwise parallel to a linear path 32 that coincides with the centralaxis of rotation 18 of drive 12. In the embodiment shown, thejoint-to-joint length of forearm or second link 20 is larger than thejoint-to-joint length of the upper arm or first link 16. In theembodiment shown, the lateral offset 38 of the end-effector or thirdlink 24 corresponds to the difference of the joint-to-joint lengths ofthe forearm 20 and upper arm 14. As will be described in greater detailbelow, the lateral offset 38 is maintained substantially constant duringextension and retraction of arm 14 such that substrate 28 is moved alonga linear path without rotation of substrate 28 or end effector 24 withrespect to the linear path. This is accomplished with structure internalto arm 14 as will be described without the use of an additionalcontrolled axis to control rotation of end effector 24 at wrist 26 withrespect to forearm 20. In one aspect of the disclosed embodiment, withrespect to FIG. 1A, the center of mass of the third link or end effector24 may reside at the wrist centerline or axis of rotation 26.Alternately, the center of mass of the third link or end effector 24 mayreside along path 40 offset 38 from the central axis of rotation 18. Inthis manner, the disturbance to the bands that constrain end effector 24with respect to links 16, 18 may be minimized due to a moment applied asa result of the mass being offset otherwise during extension andretraction of the arm. Here, the center of mass may be determined withor without the substrate or may be in between. Alternately, the centerof mass of the third link or end effector 24 may reside at any suitablelocation. In the embodiment shown, substrate transport apparatus 10transports substrate 28 with moveable arm assembly 14 coupled to drivesection 12 on central axis of rotation 18. Substrate support 24 iscoupled to the arm assembly 14 on wrist axis of rotation 26 where armassembly 14 rotates about central axis of rotation 18 during extensionand retraction as will be seen with respect to FIGS. 3A-C. Wrist axis ofrotation 26 moves along wrist path 40 parallel to and offset 38 orotherwise from radial path, for example, path 30, 34 or 36 relative tothe central axis of rotation 18 during extension and retraction.Substrate support 24 similarly moves parallel to radial path 30 duringextension and retraction without rotation. As will be described ingreater detail in other aspects of the disclosed embodiment, theprinciples and structure that constrain the end effector to move in asubstantially purely radial motion may be applied where the length ofthe fore arm is shorter than that of the upper arm. Further, thefeatures may be applied where more than one substrate is being handledby the end effector. Further, the features may be applied where a secondarm is used in connection with the drive handling one or more additionalsubstrates. Accordingly, all such variations may be embraced.

Referring also to FIGS. 2A and 2B, there are shown partial schematic topand side views respectively of system 10 showing the internalarrangements used to drive the individual links of arm 14 shown in FIGS.1A and 1B. Drive 12 has first and second motors 52, 54 withcorresponding first and second encoders 56, 58 coupled to housing 60 andrespectively driving first and second shafts 62, 64. Here shaft 62 maybe coupled to pulley 66 and shaft 64 may be coupled to upper arm 64where shafts 62, 64 may be concentric or otherwise disposed. Inalternate aspects, any suitable drive may be provided. Housing 60 may bein communication with chamber 68 where bellows 70, chamber 68 and aninternal portion of housing 60 isolate a vacuum environment 72 from anatmospheric environment 74. Housing 60 may slide in a z direction as acarriage on slides 76 where a lead screw or other suitable vertical orlinear z drive 78 may be provided to selectively move housing 60 and arm14 coupled there to in a z 80 direction. In the embodiment shown, upperarm 16 is driven by motor 54 about the central axis of rotation 18.Similarly, forearm is driven by motor 52 through a band drive havingpulleys 66, 82 and bands 84, 86 such as conventional circular pulleysand bands. In alternate aspects, any suitable structure may be providedto drive forearm 20 with respect to upper arm 16. The ratio betweenpulleys 66 and 82 may be 1:1, 2:1 or any suitable ratio. Third link 24with the end-effector may be constrained by a band drive having pulley88 grounded with respect to link 16, pulley 90 grounded with respect toend effector or third link 24 and bands 92, 94 constraining pulley 88and pulley 90. As will be described, the ratio between pulleys 88, 90may not be constant in order for third link 24 to track a radial pathwithout rotation during extension and retraction of arm 14. This may beaccomplished where pulleys 88, 90 may be one or more non circularpulleys, such as two non-circular pulleys or where one of pulley 88, 90may be circular and the other being non circular. Alternately, anysuitable coupling or linkage may be provided to constrain the path ofthird link or end effector 24 as described. In the embodiment shown, atleast one non-circular pulley compensates for the effects of the unequallengths of upper arm 16 and forearm 20 so that the end-effector 24points radially 30 regardless of the position of the first two links 16,20. The embodiment will be described with respect to pulley 90 being noncircular and pulley 88 being circular. Alternately, pulley 88 may benon-circular and pulley 90 circular. Alternately, pulleys 88 and 92 maybe non-circular or any suitable coupling may be provided to constrainthe links of arm 14 as described. By way of example, non-circularpulleys or sprockets are described in U.S. Pat. No. 4,865,577 issued onSep. 12, 1989 and entitled Noncircular Drive which is herebyincorporated by reference herein in its entirety. Alternately, anysuitable coupling may be provided to constrain the links of arm 14 asdescribed, for example, any suitable variable ratio drive or coupling,linkage gears or sprockets, cams or otherwise used alone or incombination with a suitable linkage or other coupling. In the embodimentshown, elbow pulley 88 is coupled to upper arm 16 and is shown round orcircular where wrist pulley 90 coupled to wrist or third link 24 isshown non circular. The wrist pulley shape is non-circular and may havesymmetry about a line 96 perpendicular to the radial trajectory 30 whichalso may coincide with or be parallel to the line between the twopulleys 88, 90 when the forearm 20 and upper arm 16 are lined up overeach other with the wrist axis 26 closest to shoulder axis 18, forexample as seen in FIG. 3B. The shape of pulley 90 is such that bands92, 94 stay tight as arm 14 extends and retracts establishing points oftangency 98, 100 on opposing sides of pulley 90 having changing radialdistances 102, 104 from the wrist axis of rotation 26. For example, atthe orientation shown in FIG. 3B, each of the points of tangency 98, 100of the two bands on the pulley is at an equal radial distance 102, 104from the wrist axis of rotation 26. This will be further described withrespect to FIG. 4 showing respective ratios. In order for arm 14 torotate, both drive shafts 62, 64 of the robot need to move in thedirection of rotation of the arm by the same amount. In order for theend-effector 24 to extend and refract radially along a straight-linepath, the two drive shafts 62, 64 need to move in a coordinated manner,for example, in accordance with the exemplary inverse kinematicequations presented later in this section. Here, a substrate transportapparatus 10 is adapted to transport substrate 28. Forearm 20 isrotatably coupled to upper arm 16 and rotatable about elbow axis 22being offset from central axis 18 by an upper arm link length. Endeffector 24 is rotatably coupled to forearm 20 and rotatable about wristaxis 26 offset from the elbow axis 22 by a forearm link length. Wristpulley 90 is fixed to the end effector 24 and coupled to elbow pulley 88with band 92, 94. Here, the forearm link length is different than theupper arm link length and the end effector is constrained with respectto the upper arm by the elbow pulley, the wrist pulley and the band suchthat the substrate moves along a linear radial path 30 with respect tothe central axis 18. Here, substrate support 24 coupled to the upper arm16 with a substrate support coupling 92 and driven about the wrist axisof rotation 26 by relative movement between the forearm 20 and the upperarm 16 about the elbow axis of rotation 22. FIGS. 3A, 3B and 3Cillustrate extension motion of the robot of FIGS. 1 and 2. FIG. 3A showsthe top view of the robot 10 with the arm 14 in its retracted position.FIG. 3B depicts the arm 14 partially extended with the forearm 20aligned on top of the upper arm 16, illustrating that the lateral offset38 of the end-effector corresponds to the difference of thejoint-to-joint lengths of the forearm 20 and upper arm 16. FIG. 3C showsthe arm 14 in an extended position although not full extension.

Exemplary direct kinematics may be provided. In alternate aspects, anysuitable direct kinematics may be provided to correspond to alternativestructure. The following exemplary equations may be used to determinethe position of the end-effector as a function of the position of themotors:

x ₂ =l ₁ cos θ₁ +l ₂ cos θ₂  (1.1)

y ₂ =l ₁ sin θ₁ +l ₂ sin θ₂  (1.2)

R ₂=sqrt(x ₂ ² +y ₂ ²)  (1.3)

T ₂ =a tan 2(y ₂ ,x ₂)  (1.4)

α₃ =a sin(d ₃ /R ₂) where d ₃ =l ₂ −l ₁  (1.5)

α₁₂=θ₁−θ₂  (1.6)

If α₁₂ <π: R=sqrt(R ₂ ² −d ₃ ²)+l ₃ , T=T ₂+α₃, else R=−sqrt(R ₂ ² −d ₃²)+l ₃ , T=T ₂−α₃+π  (1.7)

Exemplary inverse kinematics may be provided. In alternate aspects, anysuitable inverse kinematics may be provided to correspond to alternativestructure. The following exemplary equations may be utilized todetermine the position of the motors to achieve a specified position ofthe end-effector:

x ₃ =R cos T  (1.8)

y ₃ =R sin T  (1.9)

x ₂ =x ₃ −l ₃ cos T+d ₃ sin T  (1.10)

y ₂ =y ₃ −l ₃ sin T−d ₃ cos T  (1.11)

R ₂=sqrt(x ₂ ² +y ₂ ²)  (1.12)

T ₂ =a tan 2(y ₂ ,x ₂)  (1.13)

α₁ =a cos((R ₂ ² +l ₁ ² −l ₂ ²)/(2R ₂ l ₁))  (1.14)

α₂ =a cos((R ₂ ² −l ₁ ² +l ₂ ²)/(2R ₂ l ₂))  (1.15)

If R>l ₃:θ₁ =T ₂+α₁,θ₂ =T ₂−α₂, else: θ₁ =T ₂−α₁,θ₂ =T ₂+α₂  (1.16)

The following nomenclature may be used in the kinematic equations:

-   -   d₃=lateral offset of end-effector (m)    -   l₁=join-to-joint length of first link (m)    -   l₂=joint-to-joint length of second link (m)    -   l₃=length of third link with end-effector, measured from wrist        joint to reference point on end-effector (m)

R=radial position of end-effector (in)

-   -   R₂=radial coordinate of wrist joint (m)    -   T=angular position of end-effector (rad)    -   T₂=angular coordinate of wrist joint (rad)    -   x₂=x-coordinate of wrist joint (m)    -   x₃=x-coordinate of end-effector (m)    -   y₂=y-coordinate of wrist joint (m)    -   y₃=y-coordinate of end-effector (m)    -   θ₁=angular position of drive shaft coupled to first link (rad)    -   θ₂=angular position of drive shaft coupled to second link (rad).

The above exemplary kinematic equations may be used to design a suitabledrive, for example, a band drive that constraints the orientation of thethird link 24 so that the end-effector 24 points radially 30 regardlessof the position of the first two links 16, 20 of the arm 14.

Referring to FIG. 4, there is shown a plot 120 of the transmission ratior₃₁ 122 of the band drive that constraints the orientation of the thirdlink as a function of normalized extension of the arm measured from thecenter of the robot to the root of the end-effector, i.e., (R−l₃)/l₁.The transmission ratio r₃₁ is defined as a ratio of the angular velocityof the pulley attached to the third link, ω₃₂, over the angular velocityof the pulley attached to the first link, ω₁₂, both defined relative tothe second link. The figure graphs the transmission ratio r₃₁ fordifferent l₂/l₁ (from 0.5 to 1.0 with increment of 0.1, and from 1.0 to2.0 with increment of 0.2). The profile of the non-circular pulley(s)may be calculated to achieve the transmission ratio r₃₁ in accordancewith FIG. 4, for example, the profile depicted in FIGS. 2A, 54A and 54B.

In the disclosed embodiment, a longer reach may be obtained compared toan equal-link arm with the same containment volume with the use of oneor more with non-circular pulley(s) or other suitable device toconstrain the end effector motion. In alternate aspects, the first linkmay be driven by a motor either directly or via any kind of coupling ortransmission arrangement. Here, any suitable transmission ratio can beused. Alternately, the band drive that actuates the second link may besubstituted by any other arrangement with an equivalent functionality,such as a belt drive, cable drive, gear drive, linkage-based mechanismor any combination of the above. Similarly, the band drive thatconstrains the third link may be substituted by any other suitablearrangement, such as a belt drive, cable drive, non-circular gears,linkage-based mechanism or any combination of the above. Here, theend-effector may but does not need to point radially. For example, theend effector may be positioned with respect to the third link with anysuitable offset and point in any suitable direction. Further, inalternate aspects, the third link may carry more than one end-effectoror substrate. Any suitable number of end-effectors and/or materialholders can be carried by the third link. Further, in alternate aspects,the joint-to-joint length of the forearm can be smaller than thejoint-to-joint length of the upper arm, for example, as seen representedby l₂/l₁<1 in FIG. 4 and as seen and described with respect to FIGS.25-34 and 43-53.

Referring now to FIGS. 5A and 5B, there are shown top and side viewsrespectively of robot 150 incorporating some features of robot 10. Robot150 is shown having drive 12 with arm 152 shown in a retracted position.Arm 152 has features similar to that of arm 14 except as describedherein. By way of example, the joint-to-joint length of the forearm orsecond link 158 is larger than the joint-to-joint length of the upperarm or first link 154. Similarly, the lateral offset 168 of theend-effector or third link 162 corresponds to the difference of thejoint-to-joint lengths of the forearm 158 and upper arm 154. Referringalso to FIGS. 6A and 6B, there is shown drive 150 with the internalarrangements used to drive the individual links of the arm. In theembodiment shown, upper arm 154 is driven by one motor through shaft 64as described with respect to arm 14 of FIGS. 1 and 2. Similarly, endeffector or third link 162 is constrained with respect upper arm 154 bya non-circular pulley arrangement as described with respect to arm 14 ofFIGS. 1 and 2. The exemplary difference between arm 152 and arm 14 isseen where forearm 158 is coupled via a band arrangement with at leastone non-circular pulley to shaft 62 and another motor of drive 12. Here,the coupling or band arrangement may have features as described hereinor as described with respect to pulley drive 88, 90 of FIGS. 1 and 2.The coupling or band arrangement has non circular pulley 202 coupled toshaft 62 of drive 12 and is rotateable about axis 18 with shaft 62. Theband arrangement of arm 152 further has circular pulley 204 coupled toupper arm, link 158 and rotatable about elbow axis 156. Circular pulley204 is coupled to non-circular pulley 202 via bands 206, 208 where bands206, 208 may be kept tight by virtue of the profile of non-circularpulley 202. In alternate aspects, any combination of pulleys or othersuitable transmission may be provided. Pulleys 202 and 204 and bands206, 208 cooperate such that rotation of upper arm 154 relative topulley 202 (for example, holding pulley 202 stationary while rotatingupper arm 154) causes wrist joint 160 to extend and retract along astraight line parallel to the desired radial path 180 of theend-effector and offset 168 from the path 180. Here, third link 162 withthe end-effector is constrained by a band drive as described withrespect to arm. 14, for example, with at least one non-circular pulleyso that the end-effector points radially 180 regardless of the positionof the first two links 154, 158. Here, any suitable coupling may beprovided to constrain the links of arm 14 as described, for example, oneor more suitable variable ratio drive or coupling, linkage gears orsprockets, cams or otherwise used alone or in combination with asuitable linkage or other coupling. In the embodiment shown, elbowpulley 204 is coupled to fore arm 158 and is shown round or circularwhere shoulder pulley 202 coupled to shaft 62 is shown non circular. Theshaft pulley shape is non-circular and may have symmetry about a line218 perpendicular to the radial trajectory 180 which also may coincidewith or be parallel to the line between the two pulleys 202, 204 whenthe forearm 158 and upper arm 154 are lined up over each other with thewrist axis 160 closest to shoulder axis 18, for example as seen in FIG.7B. The shape of pulley 202 is such that bands 206, 208 stay tight asarm 152 extends and retracts establishing points of tangency 210, 212 onopposing sides of pulley 202 having changing radial distances 214, 216from the shoulder axis of rotation 18. For example, at the orientationshown in FIG. 7B, each of the points of tangency 210, 212 of the twobands on the pulley is at an equal radial distance 214, 216 from theshoulder axis of rotation 18. This will be further described withrespect to FIG. 8 showing respective ratios. In order for arm 152 torotate, both drive shafts 62, 64 of the robot need to move in thedirection of rotation of the arm by the same amount. In order for theend-effector 162 to extend and retract radially along a straight-linepath, the two drive shafts 62, 64 need to move in a coordinated manner,for example, in accordance with the exemplary inverse kinematicequations presented later in this section, for example, the drive shaftcoupled to the upper arm needs to move according to the inversekinematic equations presented below while the other motor is keptstationary. FIGS. 7A, 7B and 7C illustrate extension motion of robot 150of FIGS. 5 and 6. FIG. 7A shows the top view of the robot with the arm152 in its retracted position. FIG. 7B depicts the arm partiallyextended with the forearm aligned on top of the upper arm, illustratingthat the lateral offset 168 of the end-effector 162 that corresponds tothe difference of the joint-to-joint lengths of the forearm 158 andupper arm 154. FIG. 7C shows the arm in an extended position althoughnot full extension.

Exemplary direct kinematics may be provided. In alternate aspects, anysuitable direct kinematics may be provided to correspond to alternativestructure. The following exemplary equations may be used to determinethe position of the end-effector as a function of the position of themotors:

d ₁ =l ₁ sin(θ₁−θ₂)  (2.1)

If (θ₁−θ₂)<π/2: θ₂₁=θ₂ −l ₂ a sin((d ₁ +d ₃)/l ₂), else θ₂₁=θ₂ +a sin((d₁ +d ₃)/l ₂)+π  (2.2)

x ₂ =l ₁ cos θ₁ +l ₂ cos θ₂₁  (2.3)

y ₂ =l ₁ sin θ₁ +l ₂ sin θ₂₁  (2.4)

R ₂=sqrt(x ₂ ² +y ₂ ²)  (2.5)

T ₂ =a tan 2(y ₂ ,x ₂)  (2.6)

If (θ₁−θ₂)<π/d2: R=sqrt(R ₂ ² −d ₃ ²)+l ₃ , T=θ ₂, else R=−sqrt(R ₂ ² −d₃ ²)+l ₃ , T=θ ₂  (2.7)

Exemplary inverse kinematics may be provided. In alternate aspects, anysuitable inverse kinematics may be provided to correspond to alternativestructure. The following exemplary equations may be utilized todetermine the position of the motors to achieve a specified position ofthe end-effector:

x ₃ =R cos T  (2.8)

y ₃ =R sin T  (2.9)

x ₂ =x ₃ −l ₃ cos T+d ₃ sin T  (2.10)

y ₂ =y ₃ −l ₃ sin T−d ₃ cos T  (2.11)

R ₂=sqrt(x ₂ ² −y ₂ ²)  (2.12)

T ₂ =a tan 2(y ₂ ,x ₂)  (2.13)

α₁ =a cos((R ₂ ² +l ₁ ² −l ₂ ²)/(2R ₂ I ₁))  (2.14)

If R>l ₃: θ₁ =T ₂+α₁, θ₂ =T, else: θ₁ =T ₂−α₁, θ₂ =T  (2.15)

The following nomenclature is used in the kinematic equations:

-   -   d₃=lateral offset of end-effector (m)    -   I₁=join-to-joint length of first link (m)    -   I₂=joint-to-joint length of second link (m)    -   l₃=length of third link with end-effector, measured from wrist        joint to reference point on end-effector (m)    -   R=radial position of end-effector (m)    -   R₂=radial coordinate of wrist joint (m)    -   T=angular position of end-effector (rad)    -   T₂=angular coordinate of wrist joint (rad)    -   x₂=x-coordinate of wrist joint (m)    -   x₃=x-coordinate of end-effector (m)    -   y₂=y-coordinate of wrist joint (m)    -   y₃=y-coordinate of end-effector (m)    -   θ₁=angular position of drive shaft coupled to first link (rad)    -   θ₂=angular position of drive shaft coupled to second link (rad).

The above kinematic equations may be used to design the band drive thatcontrols the second link 158 so that rotation of the upper arm 154causes the wrist joint 160 to extend and retract along a straight lineparallel to the desired radial path 180 of the end-effector 162.

Referring now to FIG. 8, there is shown a graph 270 that shows thetransmission ratio r₂₀ 272 of the band drive that drives the second linkas a function of normalized extension of the arm measured from thecenter of the robot to the root of the end-effector, i.e., (R−l₃) l₁.The transmission ratio r₂₀ is defined as a ratio of the angular velocityof the pulley attached to the second link, ω₂₁, over the angularvelocity of the pulley attached to the second motor, ω₀₁, both definedrelative to the first link. The figure graphs the transmission ratio r₂₀for different l₂/l₁.

The profile of the non-circular pulley(s) for the band drive that drivesthe second link is calculated to achieve the transmission ratio r₂₀ 272in accordance with FIG. 8. An example pulley profile is depicted in FIG.6A and as will be described with respect to FIGS. 55A and 55B.

The transmission ratio r₃₁ of the band drive that constraints theorientation of the third link 168 may be the same as depicted in FIG. 4for the embodiment of FIGS. 1 and 2. The transmission ratio r₃₁ isdefined as a ratio of the angular velocity of the pulley attached to thethird link, ω₃₂, over the angular velocity of the pulley attached to thefirst link, ω₁₂, both defined relative to the second link. The figuregraphs the transmission ratio r₃₁ for different l₂/l₁ (from 0.5 to 1.0with increment of 0.1, and from 1.0 to 2.0 with increment of 0.2). Theprofile of the non-circular pulley(s) for the band drive that constrainsthe third link 162 may be calculated to achieve the transmission ratior₃₁ in accordance with FIG. 4. An example pulley profile is depicted inFIG. 6A.

In the embodiment shown, a longer reach may be obtained as compared toan equal-link arm with the same containment volume while usingnon-circular pulleys or other suitable mechanism to constrain the endeffector as described. As compared to the embodiment disclosed in FIGS.1 and 2, one more band drive with non-circular pulleys may be in placeof conventional one at shoulder axis 18. In alternate aspects, the firstlink may be driven by a motor either directly or via any kind ofcoupling or transmission arrangement, for example, any suitabletransmission ratio may be used. Alternately, the band drives thatactuate the second link and constrain the third link may be substitutedby any other arrangement with an equivalent functionality, such as abelt drive, cable drive, non-circular gears, linkage-based mechanism orany combination of the above. Further, the third link may be constrainedto keep the end-effector radial via a conventional two stage bandarrangement that synchronizes the third link to the pulley driven by thesecond motor, as illustrated in FIG. 9. Alternatively, the two stageband arrangement may be substituted by any other suitable arrangement,such as a belt drive, cable drive, gear drive, linkage-based mechanismor any combination of the above. In addition, the end-effector may butdoes not need to point radially. For example, the end effector may bepositioned with respect to the third link with any suitable offset andpoint in any suitable direction. In alternate aspects, the third linkmay carry more than one end-effector or substrate. Here, any suitablenumber of end-effectors and/or material holders can be carried by thethird link. Further, the joint-to-joint length of the forearm may besmaller than the joint-to-joint length of the upper arm, for example, asrepresented by l₂/l₁<1 in FIG. 8.

Referring now to FIG. 9, there is shown an alternative robot 300 wherethe third link may be constrained to keep the end-effector radial via aconventional two stage band arrangement that synchronizes the third linkto the pulley driven by the second motor. Robot 300 is shown havingdrive 12 and arm 302. Arm 302 may have upper arm or first link 304coupled to shaft 64 and rotatable about central or shoulder axis 18. Arm302 has forearm or second link 308 rotateably coupled to upper arm 304at elbow axis 306. Links 304, 308 may have unequal lengths as previouslydescribed. Third link or end effector 312 is rotatably coupled to thesecond link or forearm 308 at wrist axis 310 where end effector 312 maytransport a substrate 28 along a radial path without rotation with links304, 308 having unequal link lengths as previously described. In theembodiment shown, shaft 62 is coupled to two pulleys, 314, 316 wherepulley 314 may be circular and where pulley 316 may be non-circular.Here, circular pulley 314 constrains the third link 312 to keep theend-effector 312 radial via a conventional two stage 318, 320 circularband arrangement that synchronizes the third link 312 to the pulleydriven by shaft 314. The two stage arrangement 318, 320 has pulley 314coupled by bands 322 to elbow pulley 324 that is coupled to elbow pulley326 where elbow pulley 326 is coupled to wrist pulley 328 via bands 330.Forearm 308 may further have elbow pulley 332 that may be circular andcoupled to shoulder pulley 316 through bands 334 where shoulder pulleymay be non-circular and coupled to pulley 314 and shaft 62.

The disclosed embodiment may be further embodied with respect to robotshaving robot drives with additional axis and where the arms coupled tothe robot drive may have independently operable additional end effectorscapable of carrying one or more substrates. By way of example, arms withtwo independently operable arms linkages or “dual arm” configurationsmay be provided where each independently operable arm may have an endeffector adapted to support one, two or any suitable number ofsubstrates. Here and as will be described below, each independentlyoperable arm may have first and second links having different linklengths and where the end effector and supported substrate coupled tothe links operate and track as described above. Here, a substratetransport apparatus may transport first and second substrates and havingfirst and second independently moveable arm assemblies coupled to adrive section on a common axis of rotation. First and second substratesupports are coupled to the first and second arm assemblies respectivelyon first and second wrist axis of rotation. One or both of the first andsecond arm assemblies rotate about the common axis of rotation duringextension and retraction. The first and second wrist axis of rotationmove along first and second wrist paths parallel to and offset from aradial path relative to the common axis of rotation during extension andretraction. The first and second substrate supports move parallel to theradial path during extension and retraction without rotation. Variationson the disclosed embodiment having multiple and independently operablearms are provided below where in alternate aspects any suitablecombination of features may be provided.

Referring now to FIGS. 10A and 10B, there are shown top and side viewsrespectively of robot 350 with a dual arm arrangement. Robot 350 has arm352 having a common upper arm 354 and independently operable forearms356, 358 each having respective end effectors 360, 362. In theembodiment shown, both linkages are shown in their retracted positions.The lateral offset of the end-effectors 366 corresponds to thedifference of the joint-to-joint lengths of the forearm 354 and upperarms 356, 358. In the embodiment shown, the upper arms may have the samelength and being longer than the forearm. Further, end effectors 360,362 are positioned above forearms 356, 358. Referring now to FIGS. 11Aand 11B show top and side views respectively of a robot 375 with the armin an alternative configuration. In the embodiment shown, arm 377 mayhave features as described with respect to FIGS. 10A and 10B with bothlinkages are shown in their retracted positions. In this configuration,the third link with the end-effector 382 of the upper linkage issuspended underneath the forearm 380 to reduce vertical spacing betweenthe two end-effectors 382, 384. Here, a similar effect may be achievedby stepping 368 the top end-effector 360 of the configuration of FIGS.10A and 10B down. Referring also to FIGS. 12 and 13 there is shown theinternal arrangements of robots 350, 375 respectively used to drive theindividual links of the arms of FIGS. 10 and 11, respectively. In theembodiment shown, drive 390 may have first second and third drivingmotors 392, 394, 396 that may be rotor stator arrangements drivingconcentric shafts 398, 400, 402 respectively and having positionencoders 404, 406, 408 respectively. Z drive 410 may drive the motors ina vertical direction where the motors may be contained partially orcompletely within housing 412 and where bellows 414 seals an internalvolume of housing 412 to chamber 416 and where the internal volume andan interior of chamber 416 may operate within an isolated environmentsuch as vacuum or otherwise. In the embodiment shown, the common upperarm 354 is driven by one motor 396. Each of the two forearms 356, 358pivot on a common axis 420 at the elbow of upper arm 354 and are drivenindependently by motors 394, 396 respectively through band drives 422,424 respectively that may have conventional pulleys. The third linkswith the end-effectors 360, 362 are constrained by band drives 426, 428respectively, each with at least one non-circular pulley, whichcompensate for the effects of the unequal lengths of the upper arms andforearms. Here, the band drives in each of the linkages may be designedusing the methodology described for FIGS. 1 and 2 and where thekinematic equations presented for FIGS. 1 and 2 may also be used foreach of the two linkages of the dual arm. In order for the arm torotate, all three drive shafts 398, 400, 402 of the robot need to movein the direction of rotation of the arm by the same amount. In order forone of the end-effectors to extend and retract radially along astraight-line path, the drive shaft of the common upper arm and thedriveshaft coupled to the forearm associated with the active endeffector need to move in a coordinated manner in accordance with theinverse kinematic equations for FIGS. 1 and 2. At the same time, thedriveshaft coupled to the other forearm needs to rotate in synch withthe drive shaft of the common upper arm in order for the inactiveend-effector to remain refracted. Referring also to FIGS. 14A, 14B and14C there is shown the arm of FIGS. 11A and 11B as the upper and lowerlinkages extend. Here, the inactive linkage 356, 360 rotates while theactive linkage 358, 362 extends. By way of example, the upper linkage358, 362 rotates as the lower linkage 356, 360 extends, and the lowerlinkage 356, 360 rotates as the upper linkage 358, 362 extends. In thedisclosed embodiment of FIGS. 10 and 11, set up and control may besimplified where the arm arrangement may be used on a coaxial drive withno dynamic seals while providing a longer reach compared to equal-linklength arms with the same containment volume. Here, no bridge is used tosupport any of the end-effectors. In the embodiment shown, the inactivearm rotates while the active one extends. One of the wrist jointstravels above the lower end-effector (closer to wafer than in anequal-link arrangement).

Referring now to FIGS. 15A and 15B, there are shown top and side viewsrespectively of robot 450 with a dual arm arrangement. Robot 450 has arm452 having a common upper arm 454 and independently operable forearms456, 458 each having respective end effectors 460, 462. In theembodiment shown, both linkages are shown in their retracted positions.The lateral offset of the end-effectors 466 corresponds to thedifference of the joint-to-joint lengths of the forearm 454 and upperarms 456, 458. In the embodiment shown, the upper arms may have the samelength and being longer than the forearm. Further, end effectors 460,462 are positioned above forearms 456, 458. Referring also to FIGS. 16Aand 16B show the top and side views of the robot 475 with the arm in analternative configuration. Again, both linkages are shown in theirretracted positions. In this configuration, the third link and theend-effector 482 of the left linkage is suspended underneath the forearm480 to reduce vertical spacing between the two end-effectors 482, 484. Asimilar effect can be achieved by stepping 468 the top end-effector ofthe configuration of FIGS. 15A and 15B down. Alternatively, a bridge canbe used to support one of the end-effectors. The combined upper arm link454 may be a single piece as depicted in FIGS. 15 and 16 or it can beformed by two or more sections 470, 472, as shown in the example ofFIGS. 17A and 17B. Here, a two-section design may be provided as lighterand using less material, with the left 472 and right 470 sections may beidentical components. Here, a two piece design may also have provisionsfor adjustment of the angular offset between the left and rightsections, which may be convenient when different retracted positionsneed to be supported. Referring also to FIGS. 18 and 19, there is shownthe internal arrangements used to drive the individual links of the armof FIGS. 15 and 16, respectively. The combined upper arm 554 is showndriven by one motor with shaft 402. Each of the two forearms 456, 458 isdriven independently by one motor each via shafts 400, 398 respectivelythrough band drives 490, 492 with conventional pulleys. Here, links 456,458 rotate on separate axis' 494, 496 respectively. The third links withthe end-effectors 460, 462 are constrained by band drives 498, 500respectively, each with at least one non-circular pulley, whichcompensate for the effects of the unequal lengths of the upper arms andforearms. Here, band drives 498, 500 in each of the linkages 456, 460and 458, 462 are designed using the methodology described for FIGS. 1and 2. Here, the kinematic equations presented for FIGS. 1 and 2 mayalso be used for each of the two linkages 456, 460 and 458, 462 of thedual arm. In order for the arm 452 to rotate, all three drive shafts398, 400, 402 of the robot need to move in the direction of rotation ofthe arm by the same amount. In order for one of the end-effectors toextend and retract radially along a straight-line path, the drive shaftof the common upper arm and the driveshaft coupled to the forearmassociated with the active end effector need to move in a coordinatedmanner in accordance with the inverse kinematic equations presented withrespect to FIGS. 1 and 2. At the same time, the driveshaft coupled tothe other forearm needs to rotate in synch with the drive shaft of thecommon upper arm in order for the inactive end-effector to remainretracted. Referring also to FIGS. 20A, 20B and 20C, there is shown thearm of FIGS. 16A and 16B as the left 458, 462 and right 456, 460linkages extend. Note that the inactive linkage 456, 460 rotates whilethe active linkage 458, 462 extends. Here, the right linkage 456, 460rotates as the left linkage 458,462 extends, and the left linkage 458,462 rotates as the right linkage 456, 460 extends. The embodiment shownleverages the benefits of a solid link design being easy to set up andcontrol and the coaxial drive, for example, with no dynamic seals whileproviding a longer reach compared to equal-link arms with the samecontainment volume. Here, no bridge is used to support any of theend-effectors. Here, the inactive arm rotates while the active oneextends. One of the wrist joints travels above the lower end-effector,closer to the wafer than in an equal-link arrangement. This can beavoided by using a bridge (not shown) to support the top end-effector.In this case, the unsupported length of the bridge may be longercompared to an equal-link arm design. Further, the retract angle may bemore difficult to change compared to the configuration with common elbowjoint, for example, as seen in FIGS. 10 and 11 and independent dual arm,for example, as seen in FIGS. 21 and 22.

Referring now to FIGS. 21A and 21B, there is shown top and side viewsrespectively of robot 520 with independent dual arms 522, 524. In theembodiment shown, both linkages 522, 524 are shown in their retractedpositions. Arm 522 has independently operable upper arm 526, forearm 528and third link with end effector 530. Arm 524 has independently operableupper arm 532, forearm 534 and third link with end effector 536. In theembodiment shown, forearms 528, 534 are shown longer than upper arms526, 532 where end effectors 530, 536 are positioned above forearms 528,534 respectively. Referring also to FIGS. 22A and 22B show the top andside views of robot 550 with features similar to that of robot 520 withthe arm in an alternative configuration and with both linkages shown intheir retracted positions. In this configuration, the third link and theend-effector 552 of the left linkage is suspended underneath the forearm554 to reduce vertical spacing between the two end-effectors. A similareffect can be achieved by stepping the top end-effector of theconfiguration of FIG. 21 down. Alternatively, a bridge can be used tosupport one of the end-effectors. In FIGS. 21 and 22, the right upperarm 532 is located below the left upper arm 526. Alternatively, the leftupper may be located above the right upper arm, for example, where onelinkage can be nested within the other. Referring also to FIG. 23, thereis shown the internal arrangements used to drive the individual links ofthe arm of FIGS. 21A and 21B. Here, for graphical clarity, to avoidoverlap of components, the elevations of the links are adjusted. Each ofthe two upper arms 526, 532 is driven independently by one motor eachthrough shafts 398, 402 respectively. The forearms 528, 534 are coupledvia band arrangements 570, 572, each with at least one non-circularpulley, to a third motor via shaft 400. The third links 530, 536 withthe end-effectors are constrained by band drives 574, 576, each with atleast one non-circular pulley. The band drives are designed so thatrotation of one of the upper arms 526, 532 causes the correspondinglinkage 528, 530 and 534, 536 respectively to extend and retract along astraight line while the other linkage remains stationary. The banddrives in each of the linkages may be designed using the methodologydescribed with respect to FIGS. 5 and 6 where the kinematic equationspresented for FIGS. 5 and 6 can also be used for each of the twolinkages of the dual arm. In order for the arm to rotate, all threedrive shafts 398, 400, 402 of the robot need to move in the direction ofrotation of the arm by the same amount. In order for one of theend-effectors to extend and retract radially along a straight-line path,the drive shaft of the upper arm associated with the active end-effectorneeds to be rotated according to the inverse kinematic equations forFIGS. 5 and 6 and the other two drive shafts need to be kept stationary.Referring also to FIGS. 24A, 24B and 24C, there is shown the arm of FIG.22 as the left 522 and right 524 linkages extend. Note that the inactivelinkage 524 remains stationary while the active linkage 522 extends.That is, the left linkage 522 does not move while the right linkage 524extends, and the right linkage 524 does not move when the left linkage522 extends. The embodiment shown provides a longer reach compared toequal-link arm design with the same containment volume. Here, no bridgeis used to support any of the end-effectors and the inactive linkageremains stationary while the active one extends potentially leading tohigher throughput as active linkage may extend or retract faster with noload. The embodiment shown may be more complex than shown in FIGS. 15and 16 with two more band drives with non-circular pulleys in place ofconventional ones. One of the wrist joints travels above the lowerend-effector as seen in FIG. 24. This can be avoided by using a bridge(not shown) to support the top end-effector. In this case, theunsupported length of the bridge is longer compared to an equal-link armdesign.

Referring now to FIGS. 25A and 25B, there are shown top and side viewsrespectively of robot 600 with arm 602. In the embodiment shown, bothlinkages are shown in their retracted positions. The lateral offset ofthe end-effectors 604 corresponds to the difference of thejoint-to-joint lengths of the upper arm 606 and forearms 608, 612 wherein this embodiment, forearms 608, 612 are shorter than the common upperarm 606. The internal arrangements used to drive the individual links ofthe arm may be similar to FIGS. 10-13, for example as in FIG. 13 howeverthe forearms in this instance are shorter than the common upper arm.Here, the common upper arm is driven by one motor. Each of the twoforearms is driven independently by one motor through a band drive withconventional pulleys. The third links 614, 616 with the end-effectorsare constrained by band drives, each with at least one non-circularpulley, which compensate for the effects of the unequal lengths of theupper arms and forearms. The band drives in each of the linkages may bedesigned using the methodology described for FIGS. 1 and 2. Thekinematic equations presented for FIGS. 1 and 2 may also be used foreach of the two linkages of the dual arm. Referring also to FIGS. 26A,26B and 26C, there is shown the arm of FIGS. 25A and 25B as the upperlinkage 612, 616 extends. The lateral offset 604 of the end-effectorcorresponds to the difference of the joint-to-joint lengths of the upperarm and forearm, and the wrist joint travels along a straight lineoffset with respect to the trajectory of the center of the wafer by thisdifference. Note that the inactive linkage 608, 614 rotates while theactive linkage 612, 616 extends. For instance, the upper linkage rotatesas the lower linkage extends, and the lower linkage rotates as the upperlinkage extends. Here, FIG. 26A depicts the arm with both linkages inthe retracted positions. FIG. 26B shows the upper linkage 612, 616partially extended in a position where the wrist joint of the upperlinkage is closest to the wafer carried by the lower linkage. It isobserved that the wrist joint of the upper linkage does not travel overthe wafer (however, it moves in a plane above the wafer). FIG. 26Cdepicts farther extension of the upper linkage 612, 616. The embodimentshown may provide ease of to set up and control, and may be used on acoaxial or tri axial drive with no dynamic seals or other suitabledrive. Here, no bridge may be used to support any of the end-effectors.The wrist joint of the upper linkage does not travel over the wafer onthe lower end-effector, which is the case for an equal-link design(however, it moves in a plane above the wafer on the lowerend-effector). Here, the inactive arm rotates while the active oneextends. The elbow joint may be more complex which may translate to alarger swing radius or shorter reach. Here, the arm may be taller thanthat shown in FIGS. 30 and 31 and FIG. 33 due to the overlappingforearms 608, 612.

Referring now to FIGS. 27A and 27B, there is shown top and side viewsrespectively of robot 630 with arm 632. Arm 630 may have featuressimilar to that disclosed with respect to FIGS. 15-19 except theforearms 636, 640 are shown with shorter link length than the upper arm636. Both linkages are shown in their retracted positions. The lateraloffset 634 of the end-effectors 642, 646 corresponds to the differenceof the joint-to-joint lengths of the upper arm 636 and forearms 638,640. The combined upper arm link 636 may be a single piece as depictedin FIGS. 27A and 27B or it can be formed by two or more sections 636′,636″, as shown in the example of FIGS. 28A and 28B. A two-section designmay be lighter with less material and where left 636′ and right 636″sections may be identical components. Allowances for adjustment of theangular offset between the left 636′ and right 636″ sections may beprovided, for example, where different retracted positions need to besupported. The internal arrangements used to drive the individual linksof the arm 632 may be similar to that in FIGS. 15-19, for example, asseen FIG. 19. The common upper arm 636 is driven by one motor. Each ofthe two forearms 638, 640 is driven independently by one motor through aband drive with conventional pulleys. The third links with theend-effectors 642, 646 may be constrained by band drives, each with atleast one non-circular pulley, which compensate for the effects of theunequal lengths of the upper arm 636 and forearms 638, 640. The banddrives in each of the linkages may be designed using the methodologydescribed for FIGS. 1 and 2. The kinematic equations presented for FIGS.1 and 2 may also be used for each of the two linkages of the dual arm.Referring also to FIGS. 29A, 29B and 29C, there is shown the arm ofFIGS. 27A and 27B as the right, upper linkage 640, 646 extends. Thelateral offset 634 of the end-effector corresponds to the difference ofthe joint-to-joint lengths of the upper arm and forearm, and the wristjoint travels along a straight line offset with respect to thetrajectory of the center of the wafer by this difference. Here, theinactive linkage 638, 642 rotates while the active linkage 640, 646extends. For instance, the upper linkage rotates as the lower linkageextends, and the lower linkage rotates as the upper linkage extends. InFIGS. 29A, 29B and 29C, FIG. 29A depict the arm with both linkages inthe retracted positions. FIG. 29B shows the right upper linkage 640, 646partially extended in a position where the wrist joint of the rightupper linkage 640, 646 is closest to the wafer carried by the left lowerlinkage 638, 642. Here the wrist joint of the right upper 640, 646linkage does not travel over the wafer however, it moves in a planeabove the wafer. FIG. 29C depicts farther extension of the right upperlinkage 640, 646. The embodiment shown leverages the benefits of a solidlink design, ease of set up and control and the coaxial drive, forexample, no dynamic seals. No bridge is used to support any of theend-effectors. The wrist joint of the upper linkage does not travel overthe wafer on the lower end-effector, which is the case for an equal-linkdesign however, it moves in a plane above the wafer on the lowerend-effector. The inactive arm 638, 642 rotates while the active arm640, 646 extends. The retract angle is more difficult to change comparedto the configuration with common elbow joint, for example as seen inFIGS. 25A and 25B and independent dual arm, for example, as seen inFIGS. 33A and 33B. Further, the arm is shown taller than FIGS. 30 and 31and FIGS. 33A and 33B as forearm 640 is shown at a higher elevation thanforearm 638.

Referring now to FIGS. 30A and 30B, there is shown the top and sideviews respectively of robot 660 with arm 662. Arm 662 may have featuresas described with respect to FIGS. 27-29 however employing a bridge andwith the two forearms at the same elevation as will be described. Bothlinkages are shown in their retracted positions. The lateral offset 664of the end-effectors corresponds to the difference of the joint-to-jointlengths of the upper arm 66 and forearms 668, 670. The combined upperarm link 666 can be a single piece as depicted in FIGS. 30A and 30B orit can be formed by two or more sections 666′, 666″, as shown in theexample of FIGS. 31A and 31B. The internal arrangements used to drivethe individual links of the arm may be identical to that shown for FIGS.15-19 but where the forearms 668, 670 are shorter than the upper arm666. The common upper arm 666 is driven by one motor. Each of the twoforearms 668, 670 is driven independently by one motor through a banddrive with conventional pulleys. The third links with the end-effectors672, 674 are constrained by band drives, each with at least onenon-circular pulley, which compensate for the effects of the unequallengths of the upper arms and forearms. The band drives in each of thelinkages may be designed using the methodology described for FIGS. 1 and2. The kinematic equations presented for FIGS. 1 and 2 can also be usedfor each of the two linkages of the dual arm. Third link and endeffector 674 has a bridge 680 that has an upper end effector portion682, a side offset support portion 684 offset from the wrist axisbetween link 670 and link 674 and further has a lower support portion686 coupling the wrist axis to the offset support portion 684. Bridge680 allows forearms 668 and 670 to be packaged at the same level whileproviding clearance for the interleaved portions of third link and endeffector 672 (which may include the wafer) and the bridge 680 as can beseen below with respect to FIG. 32. Bridge 680 further provides anarrangement where any moving parts, for example, associated with the twowrist joints, reside below the wafer surface during transport. Referringalso to FIGS. 32A, 32B, 32C and 32D, there is shown the top view of therobot arm of FIGS. 30A and 30B as the right linkage 670, 674 extends.The lateral offset 664 of the end-effector corresponds to the differenceof the joint-to-joint lengths of the upper arm 666 and forearm 670, andthe wrist joint 690 travels along a straight line offset with respect tothe trajectory of the center of the wafer 692 by this difference. Notethat the inactive linkage 668, 672 rotates while the active linkage 670,674 extends. For instance, the upper linkage rotates as the lowerlinkage extends, and the lower linkage rotates as the upper linkageextends. In FIGS. 32A, 32B, 32C and 32D, FIG. 32A depicts the arm withboth linkages in the retracted positions. FIG. 32B shows the rightlinkage 670, 674 partially extended in a position that corresponds tothe worst-case clearance (or is close to the worst-case clearance)between the bridge 680 of the right linkage 670, 674 and theend-effector 672 of the left linkage 668, 672. FIG. 32C shows the rightlinkage 670, 674 partially extended in a position when the forearm 670is aligned with the upper arm 666. The lateral offset of theend-effector corresponds to the difference of the joint-to-joint lengthsof the upper arm and forearm. The wrist joint 690 axis travels along astraight line offset with respect to the trajectory of the center of thewafer 692 by this difference. FIG. 32D depicts farther extension of theright linkage 670, 674. The embodiment shown combines the benefits ofthe side-by-side dual scara arrangement, for example, slim profile,resulting in a shallow chamber with a small volume, the solid linkdesign and the coaxial drive. The bridge 680 on the right linkage 670,674 is much lower and its unsupported length between vertical member 684and wrist 690 is shorter than in a prior art coaxial dual scara arm andall of the joints are below the end-effectors. Here, the inactive arm668, 672 rotates while the active arm 670, 674 extends. As will bedescribed below, in other aspects of the disclosed embodiment, and armwhich does not exhibit this behavior may be provided with a differentband drives with non-circular pulleys in place of the conventional onesdisclosed here. Alternatively, the bridge that supports the topend-effector may be eliminated by utilizing an arrangement similar tothose described for FIGS. 25A and 25B and FIGS. 27 and 28 above.

Referring now to FIGS. 33A and 33B, there is shown top and side viewsrespectively of robot 700 with arm 702. Arm 702 may have featuressimilar to that of the arm shown in FIGS. 21-23 but with forearm lengthsshorter than the upper arm lengths and employing a bridge as describedwith respect to bridge 680 by way of example and with the forearmslocated at the same elevation. Both linkages are shown in theirretracted positions. In FIGS. 33A and 33B, the right upper arm 708 islocated above the left upper arm 706. Alternatively, the left upper 706may be located above the right upper arm 708. Similarly, the third linkand end-effector 716 of the right linkage 712, 716 feature a bridge thatextends over the third link and end-effector 714 of the left linkage710, 714. Alternatively, the third link and end-effector 714 of the leftlinkage 710, 714 may feature a bridge that may extend over the thirdlink and end-effector 716 of the right linkage 712, 716. The internalarrangements used to drive the individual links of the arm may besimilar to the embodiment shown in FIGS. 21-23. Each of the two upperarms 706, 708 is driven independently by one motor. The forearms 710,712 are coupled via band arrangements, each with at least onenon-circular pulley, to a third motor. The third links 714, 716 with theend-effectors are constrained by band drives, each with at least onenon-circular pulley. The band drives are designed so that rotation ofone of the upper arms 706, 708 causes the corresponding linkage toextend and retract along a straight line while the other linkage remainsstationary. The band drives in each of the linkages are designed usingthe methodology described for the embodiment shown in FIGS. 5 and 6. Thekinematic equations presented for the embodiment shown in FIGS. 5 and 6can also be used for each of the two linkages of the dual arm. Referringalso to FIGS. 34A, 34B and 34C, there is shown the arm of FIGS. 33A and33B as the right linkage 708, 712, 716 extends. Here, the inactivelinkage 706, 710, 714 remains stationary while the active linkage 712,716 extends. That is, the left linkage does not move while the rightlinkage extends, and the right linkage does not move when the leftlinkage extends. The embodiment shown combines the benefits of theside-by-side dual scara arrangement, for example, slim profile,resulting in a shallow chamber with a small volume and the coaxialdrive. The bridge on the right linkage is much lower and its unsupportedlength is shorter than in the existing coaxial dual scara arms and allof the joints are below the end-effectors. The inactive linkage remainsstationary while the active one extends potentially leading to higherthroughput as active linkage may extend or retract faster with no load.Alternatively, the bridge that supports the top end-effector may beeliminated by utilizing an arrangement similar to those described forFIGS. 25, 27 and 28.

Referring now to FIGS. 35A and 35B, there is shown top and side views ofrobot 730 with arm 732 with both linkages shown in their refractedpositions. Each linkage has a dual-holder end-effector 740, 742, eachsupporting two substrates offset from each other for a total of 4substrates supportable. The internal arrangements used to drive theindividual links of the arm 732 may be identical to FIGS. 10 and 11, forexample, FIG. 13. The common upper arm 734 is driven by one motor. Eachof the two forearms 73736, 738 is driven independently by one motorthrough a band drive with conventional pulleys. The third links with theend-effectors 740, 742 are constrained by band drives, each with atleast one non-circular pulley, which compensate for the effects of theunequal lengths of the upper arms and forearms. The embodiment shown hasforearms longer than the upper arm. Alternately, they may be shorter.The band drives in each of the linkages are designed using themethodology described for FIGS. 1 and 2. The kinematic equationspresented for FIGS. 1 and 2 may also be used for each of the twolinkages of the dual arm. Referring also to FIG. 36, there is shown thearm of FIGS. 35A and 35B as one linkage 738, 742 extends. Note that theinactive linkage 736, 740 rotates while the active linkage 738, 742extends. For instance, the upper linkage rotates as the lower linkageextends, and the lower linkage rotates as the upper linkage extends.Compared to FIGS. 37 and 38, end-effector does not need to be shaped toavoid interference with opposite elbow.

Referring now to FIGS. 37A and 37B, there is shown top and side viewsrespectively of robot with arm 750. Both linkages are shown in theirretracted positions with each linkage having a dual-holder end-effector758, 760. The combined upper arm link 752 can be a single piece asdepicted in FIGS. 37A and 37B or it can be formed by two or moresections 752′, 752″, as shown in the example of FIGS. 38A and 38B. Theinternal arrangements used to drive the individual links of the arm maybe identical to FIGS. 15-19, for example, FIG. 19. The combined upperarms 752 are driven by one motor. Each of the two forearms 754, 756 isdriven independently by one motor through a band drive with conventionalpulleys. The third links 758, 760 with the end-effectors are constrainedby band drives, each with at least one non-circular pulley, whichcompensate for the effects of the unequal lengths of the upper arms andforearms. The embodiment shown has forearms longer than the upper arm.Alternately, they may be shorter. The band drives in each of thelinkages are designed using the methodology described for FIGS. 1 and 2.The kinematic equations presented for FIGS. 1 and 2 may also be used foreach of the two linkages of the dual arm. In order for the arm torotate, all three drive shafts of the robot need to move in thedirection of rotation of the arm by the same amount. In order for one ofthe end-effector assemblies to extend and retract radially along astraight-line path, the drive shaft of the common upper arm and thedriveshaft coupled to the forearm associated with the active linkageneed to move in a coordinated manner in accordance with the inversekinematic equations for FIGS. 1 and 2. At the same time, the driveshaftcoupled to the other forearm needs to rotate in synch with the driveshaft of the common upper arm in order for the inactive linkage toremain retracted. Referring also to FIG. 39, there is shown the arm ofFIGS. 37A and 37B as one linkage 756, 760 extends. Here, the inactivelinkage 754, 758 rotates while the active linkage extends. For instance,the right linkage rotates as the left linkage extends, and the leftlinkage rotates as the right linkage extends. The embodiment shown hasno bridge. The upper wrist travels over one of the wafers on the lowerend-effector. Here, the arm and end-effectors need to be designed sothat the top elbow clears the lower end-effector.

Referring now to FIGS. 40A and 40B, there is shown top and side viewsrespectively of robot 750 with arm 752. Both linkages are shown in theirretracted positions where each linkage has a dual-holder end-effector792, 794. The internal arrangements used to drive the individual linksof the arm may be identical to FIGS. 21-23. Each of the two upper arms784, 786 is driven independently by one motor. The forearms 788, 790 arecoupled via band arrangements, each with at least one non-circularpulley, to a third motor. The third links with the end-effectors 792,794 are constrained by band drives, each with at least one non-circularpulley. The band drives are designed so that rotation of one of theupper arms causes the corresponding linkage to extend and retract alonga straight line while the other linkage remains stationary. Theembodiment shown has forearms longer than the upper arm. Alternately,they may be shorter. The band drives in each of the linkages aredesigned using the methodology described for FIGS. 5 and 6. Thekinematic equations presented for FIGS. 5 and 6 can also be used foreach of the two linkages of the dual arm. In order for the arm torotate, all three drive shafts of the robot need to move in thedirection of rotation of the arm by the same amount. In order for one ofthe end-effector assemblies to extend and retract radially along astraight-line path, the drive shaft of the upper arm associated with theactive linkage needs to be rotated according to the inverse kinematicequations for FIGS. 5 and 6, and the other two drive shafts need to bekept stationary. Referring also to FIG. 41, there is shown the arm ofFIGS. 40A and 40B as one linkage 784, 788, 794 extends. Note that theinactive linkage 786, 790, 792 may remain stationary while the activelinkage 794, 788, 794 extends. That is, the left linkage does not movewhile the right linkage extends, and the right linkage does not movewhen the left linkage extends. Alternately, the left and right linkagesmay be moved at the same time radially independently, for example asseen in FIG. 42 where the right linkage extends slightly independentlyas compared to FIG. 41. The motion of the elbow of the upper linkage maybe limited due to potential interference with a wafer on the lowerend-effector, which may limit the reach of the robot as illustrated inFIG. 41. This limitation may be mitigated by extending the lower linkageslightly to provide additional clearance and achieve full reach as shownin FIG. 42. The embodiment shown has no bridge. The wrist of the upperlinkage may travel above a wafer on the lower end-effector. Referringnow to FIGS. 43A and 43B, there is shown top and side views respectivelyof robot 810 with arm 812. Both linkages are shown in their refractedpositions with each linkage having a dual-holder end-effector 820, 822.The internal arrangements used to drive the individual links of the armmay be identical to FIGS. 10-13. The common upper arm 814 is driven byone motor. Each of the two forearms 816, 818 is driven independently byone motor through a band drive with conventional pulleys. The thirdlinks with the end-effectors 820, 822 are constrained by band drives,each with at least one non-circular pulley, which compensate for theeffects of the unequal lengths of the upper arms and forearms. In theembodiment shown, the forearms are shorter than the upper arm;alternately they may be longer. The band drives in each of the linkagesare designed using the methodology described for FIGS. 1 and 2. Thekinematic equations presented for FIGS. 1 and 2 may also be used foreach of the two linkages of the dual arm. Referring also to FIGS. 44 and45, there is shown the arm of FIGS. 43A and 43B as the upper linkage818, 822 extends. Note that the inactive linkage 816, 820 rotates whilethe active linkage 818, 822 extends. For instance, the upper linkagerotates as the lower linkage extends, and the lower linkage rotates asthe upper linkage extends. FIGS. 44 and 45 illustrate that the wristjoint 824 of the upper linkage 818, 822 does not travel over the wafers826 carried by the lower linkage 816, 820 of the arm. The embodimentshown has no bridge. Compared to FIGS. 46 and 47, the end-effector doesnot need to be shaped to avoid interference with opposite elbow.

Referring now to FIGS. 46A and 46B, there is shown top and side viewsrespectively of robot 840 with arm 842. Both linkages are shown in theirretracted positions where each linkage has a dual-holder end-effector850, 852. The combined upper arm link 844 can be a single piece asdepicted in FIGS. 46A and 46B or it can be formed by two or moresections 844′, 844″, as shown in the example of FIGS. 47A and 47B. Theinternal arrangements used to drive the individual links of the arm maybe identical to FIGS. 15-19, for example FIG. 19. The combined upperarms 844 are driven by one motor. Each of the two forearms 846, 848 isdriven independently by one motor through a band drive with conventionalpulleys. The third links with the end-effectors 850, 852 are constrainedby band drives, each with at least one non-circular pulley, whichcompensate for the effects of the unequal lengths of the upper arms andforearms. In the embodiment shown, the forearms are shorter than theupper arm; alternately they may be longer. The band drives in each ofthe linkages are designed using the methodology described for FIGS. 1and 2. The kinematic equations presented for FIGS. 1 and 2 may also beused for each of the two linkages of the dual arm. In order for the armto rotate, all three drive shafts of the robot need to move in thedirection of rotation of the arm by the same amount. In order for one ofthe end-effector assemblies to extend and retract radially along astraight-line path, the drive shaft of the common upper arm 844 and thedriveshaft coupled to the forearm associated with the active linkageneed to move in a coordinated manner in accordance with the inversekinematic equations for FIGS. 1 and 2. At the same time, the driveshaftcoupled to the other forearm needs to rotate in synch with the driveshaft of the common upper arm in order for the inactive linkage toremain retracted. Referring also to FIGS. 48 and 49, there is shown thearm of FIGS. 46A and 46B as the upper linkage 848, 852 extends. Here,the inactive linkage 846, 850 rotates while the active linkage 848, 852extends. For instance, the upper linkage rotates as the lower linkageextends, and the lower linkage rotates as the upper linkage extends.FIGS. 48 and 49 illustrate that the wrist joint 854 of the upper linkagedoes not travel over the wafers 856 carried by the lower linkage of thearm. The embodiment shown has no bridge and the wrist joint of the upperlinkage does not travel over a wafer carried by the lower linkage. Here,the inactive arm rotates less, allowing for a higher speed of motionwhen active arm extends or retracts with no load.

Referring now to FIGS. 50A and 50B, there is shown top and side views ofrobot 870 with arm 872. Both linkages are shown in their refractedpositions where each linkage has a dual-holder end-effector 880, 882.The combined upper arm link 974 can be a single piece as depicted inFIGS. 50A and 50B or it can be formed by two or more sections, as shownin the example of FIGS. 47A and 47B. The internal arrangements used todrive the individual links of the arm may be identical to FIGS. 15-19,for example, FIG. 18. The combined upper arms 874 are driven by onemotor. Each of the two forearms 876, 878 is driven independently by onemotor through a band drive with conventional pulleys. The third linkswith the end-effectors are constrained by band drives, each with atleast one non-circular pulley, which compensate for the effects of theunequal lengths of the upper arms and forearms. In the embodiment shown,the forearms are shorter than the upper arm; alternately they may belonger. The band drives in each of the linkages may be designed usingthe methodology described for FIGS. 1 and 2. The kinematic equationspresented for FIGS. 1 and 2 may also be used for each of the twolinkages of the dual arm. In order for the arm to rotate, all threedrive shafts of the robot need to move in the direction of rotation ofthe arm by the same amount. In order for one of the end-effectorassemblies to extend and retract radially along a straight-line path,the drive shaft of the common upper arm 874 and the driveshaft coupledto the forearm associated with the active linkage need to move in acoordinated manner in accordance with the inverse kinematic equationsfor FIGS. 1 and 2. At the same time, the driveshaft coupled to the otherforearm needs to rotate in synch with the drive shaft of the commonupper arm 874 in order for the inactive linkage to remain retracted.Referring also to FIG. 51, there is shown the arm of FIGS. 50A and 50Bwith one linkage 878, 882 extended. Here, the inactive linkage 876, 880rotates while the active linkage 878, 882 extends. For instance, theupper linkage rotates as the lower linkage extends, and the lowerlinkage rotates as the upper linkage extends. The embodiment shown hasshort forearm links that may be stiffer with shorter short bands andwhere the forearms are located side-by-side facilitating a shallowchamber. Here, the short links may cause more rotation of inactive armcompared to FIGS. 46 and 47 which may be addressed by longer upper arms.Bridge 884 is provided where the arm and end-effectors may be designedso that the bridge 884 clears the inactive end-effector 880 during anextension move. Here, the base of the end-effector features an angledshape 886 as shown.

Referring now to FIGS. 52A and 52B, there is shown top and side viewsrespectively of robot 900 with arm 902. Both linkages are shown in theirrefracted positions with each linkage having a dual-holder end-effector.The internal arrangements used to drive the individual links of the armmay be identical to FIGS. 21-23. Each of the two upper arms 904, 906 isdriven independently by one motor. The forearms 908, 910 are coupled viaband arrangements, each with at least one non-circular pulley, to athird motor. The third links with the end-effectors 912, 914 areconstrained by band drives, each with at least one non-circular pulley.The band drives are designed so that rotation of one of the upper arms904, 906 causes the corresponding linkage to extend and retract along astraight line while the other linkage remains stationary. In theembodiment shown, the forearms are shorter than the upper arm;alternately they may be longer. The band drives in each of the linkagesare designed using the methodology described for FIGS. 5-6. Thekinematic equations presented for FIG. 5-6 may also be used for each ofthe two linkages of the dual arm. In order for the arm to rotate, allthree drive shafts of the robot need to move in the direction ofrotation of the arm by the same amount. In order for one of theend-effector assemblies to extend and retract radially along astraight-line path, the drive shaft of the upper arm associated with theactive linkage needs to be rotated according to the inverse kinematicequations for FIGS. 5-6, and the other two drive shafts need to be keptstationary. Referring also to FIG. 53, there is shown the arm of FIGS.52A and 52B with one linkage 906, 910, 914 extended. Note that theinactive linkage 904, 908, 912 remains stationary while the activelinkage 906, 910, 914 extends with bridge 916. That is, the left linkageneed not move while the right linkage extends, and the right linkageneed not move when the left linkage extends although they may be movedradially independently. The embodiment shown has shorter links that maybe stiffer with short bands and side-by-side forearms facilitating ashallow chamber. Alternately, the forearms may be longer than upper armsin the configuration with a bridge.

Referring now to FIGS. 54-55 there is shown a coupled dual arm 930 withopposing end effectors 938, 940. FIGS. 54A and 54B show respectively thetop and side views of the robot with the arm. Both linkages are shown intheir retracted positions where the lateral offset of the end-effectorscorresponds to the difference of the joint-to-joint lengths of the upperarm 932 and forearms 934, 936. The combined upper arm link 932 can be asingle piece as depicted in FIG. 54 or it can be formed by two or moresections. By way of example, a two-section design may be lighter whereless material, and left and right sections may be identical components.The internal arrangements used to drive the individual links of the armmay be based on that shown with respect to FIGS. 18 and 19 or otherwise.The common upper arm 932 is driven by one motor. Each of the twoforearms 934, 936 is driven independently by one motor through a banddrive with conventional pulleys. The third links with the end-effectors938, 940 are constrained by band drives, each with at least onenon-circular pulley, which compensate for the effects of the unequallengths of the upper arms 934, 936 and forearm 932. The band drives ineach of the linkages are designed using the methodology described withrespect to FIG. 1 or otherwise. The kinematic equations presented forFIG. 1 can also be used for each of the two linkages of the dual arm.FIGS. 55A-55C shows the arm of FIG. 54 as the first 934, 938 and second936, 940 linkages extend from the retracted position. The lateral offsetof the end-effector corresponds to the difference of the joint-to-jointlengths of the upper arm 934, 936 and forearm 932, and the wrist joint942, 944 travels along a straight line offset with respect to thetrajectory of the center of the wafer by this difference. Note that theinactive linkage rotates while the active linkage extends. For instance,the second linkage rotates as the first linkage extends, and the firstlinkage rotates as the second linkage extends. FIG. 55A depicts the armwith both linkages in the retracted positions. FIG. 55B shows the firstlinkage 934, 938 extended. FIG. 55C depicts the second linkage 936, 940extended. The arm shown has a low profile as the forearms travel in thesame plane and the end-effectors travel in the same plane, allowing fora shallow vacuum chamber with a small volume. Since the retractedposition of the wrist of one linkage is constrained by the wrist of theother linkage, the containment radius of the arm may be large, makingthe arm particularly suitable for applications with a large number ofprocess modules where the diameter of the chamber is dictated by thesize of the slot valves. Due to its low profile, the arm may replace afrogleg-type arm with opposing end-effectors. In the embodiment shown,the forearms are shorter than the upper arm; alternately they may belonger, for example, where the forearms are in different elevations andoverlapping.

Referring to FIGS. 56-57, there is shown an independent dual arm 960with opposing end effectors 970, 972. FIGS. 56A and 56B show the top andside views of the robot with the arm. Both linkages are shown in theirretracted positions. In FIG. 56, the upper arm 962 of the first linkageis located above the upper arm 964 of the second linkage. Alternatively,the upper arm of the second linkage may be located above the upper armof the first linkage. The internal arrangements used to drive theindividual links of the arm may be based on FIG. 23 or otherwise. Here,each of the two upper arms 962, 964 may be driven independently by onemotor. The forearms 966, 968 are coupled via band arrangements, eachwith at least one non-circular pulley, to a third motor. The third linkswith the end-effectors 970, 972 are constrained by band drives, eachwith at least one non-circular pulley. The band drives are designed sothat rotation of one of the upper arms causes the corresponding linkageto extend and retract along a straight line while the other linkageremains stationary. The band drives in each of the linkages are designedusing the methodology described for FIG. 5. The kinematic equationspresented for FIG. 5 can also be used for each of the two linkages ofthe dual arm. FIGS. 57A-57C show the arm of FIG. 56 as the first 962,966, 970 and second 964, 968, 972 linkages extend from the retractedposition. Here, that the inactive linkage remains (but not need do so)stationary while the active linkage extends. That is, the second linkagedoes not move while the first linkage extends, and the first linkagedoes not move when the second linkage extends. The arm has a low profileas the forearms travel in the same plane and the end-effectors travel inthe same plane, allowing for a shallow vacuum chamber with a smallvolume. Since the retracted position of the wrist of one linkage isconstrained by the wrist of the other linkage, the containment radius ofthe arm is large, making the arm particularly suitable for applicationswith a large number of process modules where the diameter of the chamberis dictated by the size of the slot valves. Due to its low profile, thearm can replace a frogleg-type arm with opposing end-effectors. In theembodiment shown, the forearms are shorter than the upper arm;alternately they may be longer, for example, where the forearms are indifferent elevations and overlapping.

Referring now to FIG. 58, there is shown a coupled dual arm 990 withangularly offset end effectors 998, 1000. FIGS. 58A and 58B show the topand side views of the robot with the arm. Both linkages are shown intheir refracted positions. The lateral offset 1002, 1004 of theend-effectors corresponds to the difference of the joint-to-jointlengths of the upper arm 994, 996 and forearm 992. The combined upperarm link 992 can be a single piece as depicted in FIG. 59 or it can beformed by two or more sections. The internal arrangements used to drivethe individual links of the arm are based on FIGS. 18 and 19 orotherwise. Here, the common upper arm 992 may be driven by one motor.Each of the two forearms 994, 996 may be driven independently by onemotor through a band drive with conventional pulleys. The third linkswith the end-effectors 998, 1000 are constrained by band drives, eachwith at least one non-circular pulley, which compensate for the effectsof the unequal lengths of the upper arms and forearms. The band drivesin each of the linkages are designed using the methodology described forFIG. 1 or otherwise. The kinematic equations presented for FIG. 1 canalso be used for each of the two linkages of the dual arm. Referringalso to FIGS. 59A-C, there is shown the arm of FIG. 58 as the left 994,998 and right 996, 1000 linkages extend. The lateral offset 1002, 1004of the end-effector corresponds to the difference of the joint-to-jointlengths of the upper arm and forearm, and the wrist joint travels alonga straight line offset with respect to the trajectory of the center ofthe wafer by this difference. Here, the inactive linkage rotates whilethe active linkage extends. For instance, the right linkage rotates asthe left linkage extends, and the left linkage rotates as the rightlinkage extends. FIG. 59A depicts the arm with both linkages in theretracted positions. FIG. 59B shows the left linkage 994, 998 extended.FIG. 59C depicts the right linkage 996, 1000 extended. Here, theinactive arm rotates while the active one extends. In the embodimentshown, the forearms are shorter than the upper arm; alternately they maybe longer, for example, where the forearms are in different elevationsand overlapping. In the embodiment shown, the end effectors may be 90degrees apart; alternately any separation angle may be provided.

Referring now to FIG. 60, there is shown and independent dual arm 1030with angularly offset end effectors 1040, 1042. Here, FIGS. 60A and 60Bshow the top and side views of the robot with the arm. Both linkages areshown in their retracted positions. In FIG. 60, the right upper arm 1034is located below the left upper arm 1032. Alternatively, the left uppermay be located below the right upper arm. The internal arrangements usedto drive the individual links of the arm may be based on FIG. 23. Eachof the two upper arms 1032, 1034 may be driven independently by onemotor each. The forearms are coupled via band arrangements, each with atleast one non-circular pulley, to a third motor. The third links withthe end-effectors 1040, 1042 are constrained by band drives, each withat least one non-circular pulley. The band drives are designed so thatrotation of one of the upper arms 1032, 1034 causes the correspondinglinkage to extend and refract along a straight line while the otherlinkage remains stationary. The band drives in each of the linkages aredesigned using the methodology described for FIG. 5 or otherwise. Thekinematic equations presented for FIG. 5 can also be used for each ofthe two linkages of the dual arm. FIG. 61A-61C shows the arm of FIG. 60as the left 1032, 1036, 1040 and then the right 1034, 1038, 1042 linkageextends. Here, the inactive linkage remains (but need not do so)stationary while the active linkage extends. That is, the left linkagedoes not move while the right linkage extends, and the right linkagedoes not move when the left linkage extends. Here, the inactive linkageremains stationary while the active one extends. In the embodimentshown, the forearms are shorter than the upper arm; alternately they maybe longer, for example, where the forearms are in different elevationsand overlapping. In the embodiment shown, the end effectors may be 90degrees apart; alternately any separation angle may be provided.

By way of example with respect to FIG. 62 or otherwise, the third linkand end-effector 1060, 1062, each of which may be referred to as athird-link assembly, may be designed so that the center of mass 1064,1066 is on or close to the straight-line trajectory of the wrist joint1068, 1070 respectively as the corresponding linkage of the arm extendsand retracts. This reduces the moment due to the inertial force actingat the center of mass of the third-link assembly and the reaction forceat the wrist joint, thus reducing the load on the band arrangement thatconstraints the third-link assembly. Here, the third-link assembly mayfurther be designed so that its center of mass is on one side of thewrist joint trajectory when payload is present and on the other side ofthe trajectory when no payload is present. Alternatively, the third-linkassembly may be designed so that its center of mass is substantially onthe wrist joint trajectory when payload is present as the beststraight-line tracking performance is typically required with thepayload on, as illustrated in FIG. 62. In FIG. 62, 1L is thestraight-line trajectory of the center of the wrist joint of the leftlinkage, 2L is the center 1070 of the wrist joint of the left linkage,3L is the center of mass 1066 of the third-link assembly of the leftlinkage, 4L is the force acting on the third-link assembly of the leftlinkage as the left linkage accelerates at the beginning of an extendmove (or decelerates at the end of a retract move), and 5L is theinertial force acting at the center of mass of the third-link assemblyof the left linkage as the left linkage accelerates at the beginning ofan extend move (or decelerates at the end of a retract move). Similarly,1R is the straight-line trajectory of the center of the wrist joint ofthe right linkage, 2R is the center 1068 of the wrist joint of the rightlinkage, 3R is the center of mass 1064 of the third-link assembly of theright linkage, 4R is the force acting on the third-link assembly of theright linkage as the right linkage decelerates at the end of an extendmove (or accelerates at the beginning of a retract move), and 5R is theinertial force acting at the center of mass of the third-link assemblyof the right linkage as the right linkage decelerates at the end of anextend move (or accelerates at the beginning of a retract move). In theembodiment shown, dual wafer end effectors are provided. In alternateaspects, any suitable end effector and arm or link geometry may beprovided.

In alternate aspects; the upper arms in any of the aspects of theembodiment can be driven by a motor either directly or via any kind ofcoupling or transmission arrangement. Any transmission ratio may beused. Alternately, the band drives that actuate the second link andconstrain the third link can be substituted by any other arrangement ofequivalent functionality, such as a belt drive, cable drive, circularand non-circular gears, linkage-based mechanisms or any combination ofthe above. Alternately, for example, in the dual and quad arm aspects ofthe embodiment, the third link of each linkage can be constrained tokeep the end-effector radial via a conventional two stage bandarrangement that synchronizes the third link to the pulley driven by thesecond motor, similarly to the single arm concept of FIG. 9.Alternatively, the two stage band arrangement can be substituted by anyother suitable arrangement, such as a belt drive, cable drive, geardrive, linkage-based mechanism or any combination of the above.Alternately, the upper arms in the dual and quad arm aspects of theembodiment may not be arranged in a coaxial manner. They can haveseparate shoulder joints. The two linkages of the dual and quad arms donot need to have the same length of the upper arms and the same lengthof the forearms. The length of the upper arm of one linkage may bedifferent from the length of the upper arm of the other linkage, and thelength of the forearm of one linkage may be different from the length ofthe forearm of the other linkage. The forearm-to-upper-arm ratios canalso be different for the two linkages. In the dual and quad arm aspectsof the embodiment that have different elevations of the links of theleft and right linkages, the left and right linkages can beinterchanged. The two linkages of the dual and quad arms do not need toextend along the same direction. The arms can be configured so that eachlinkage extends in a different direction. The two linkages in any of theaspects of the embodiment may consist of more or less than three links(first link=upper arm, second link=forearm, third link=link withend-effector). In the dual and quad arm aspects of the embodiment, eachlinkage may have a different number of links. In the single arm aspectsof the embodiment, the third link can carry more than one end-effector.Any suitable number of end-effectors and/or material holders can becarried by the third link. Similarly, in the dual arm aspects of theembodiment, each linkage can carry any suitable number of end-effectors.In either case, the end-effectors can be positioned in the same plane,stacked above each other, arranged in a combination of the two orarranged in any other suitable manner. Further, for dual armconfigurations, each arm may be independently operable, for example,independently in rotation, extension and/or z (vertical), for example,as described with respect to pending U.S. patent application Having Ser.No. 13/670,004 entitled “Robot System with Independent Arms” havingfiling date Nov. 6, 2012 which is herein incorporated by reference inits entirety. Accordingly all such modifications, combinations andvariations are embraced.

In accordance with one aspect of the exemplary embodiment, a substratetransport apparatus is adapted to transport a substrate. The substratetransport apparatus has a moveable arm assembly coupled to the drivesection on a central axis of rotation. A substrate support is coupled tothe arm assembly on a wrist axis of rotation. The arm assembly rotatesabout the central axis of rotation during extension and retraction. Thewrist axis of rotation moves along a wrist path parallel to and offsetfrom a radial path relative to the central axis of rotation duringextension and retraction. The substrate support moves parallel to theradial path during extension and retraction without rotation.

In accordance with another aspect of the exemplary embodiment, asubstrate transport apparatus is adapted to transport first and secondsubstrates. The substrate transport apparatus has first and secondindependently moveable arm assemblies coupled to the drive section on acommon axis of rotation. First and second substrate supports are coupledto the first and second arm assemblies respectively on first and secondwrist axis of rotation. The first and second arm assemblies rotate aboutthe common axis of rotation during extension and retraction. The firstand second wrist axis of rotation move along first and second wristpaths parallel to and offset from a radial path relative to the commonaxis of rotation during extension and retraction. The first and secondsubstrate supports move parallel to the radial path during extension andretraction without rotation.

In accordance with another aspect of the exemplary embodiment, asubstrate transport apparatus is adapted to transport a substrate. Thesubstrate transport apparatus has a drive section and an upper armrotatably coupled to the drive section, the upper arm rotatable about acentral axis. An elbow pulley is fixed to the upper arm. A forearm isrotatably coupled to the upper arm, the forearm rotatable about an elbowaxis, the elbow axis offset from the central axis by an upper arm linklength. An end effector is rotatably coupled to the forearm, the endeffector rotatable about a wrist axis, the wrist axis offset from theelbow axis by a forearm link length, the end effector supporting thesubstrate. A wrist pulley is fixed to the end effector, the wrist pulleycoupled to the elbow pulley with a band. The forearm link length isdifferent than the upper arm link length. The end effector isconstrained with respect to the upper arm by the elbow pulley, the wristpulley and the band such that the substrate moves along a linear radialpath with respect to the central axis.

In accordance with another aspect of the exemplary embodiment, asubstrate transport apparatus is adapted to transport a substrate. Thesubstrate transport apparatus has a drive section having first andsecond rotary drives. An upper arm is rotatably coupled to the firstrotary drive on a central axis of rotation. A forearm is rotatablycoupled to the upper arm, the forearm rotatable about an elbow axis ofrotation of the upper arm, the elbow axis of rotation offset from thecentral axis of rotation by an upper arm link length. The forearm isfurther coupled to the second rotary drive with a forearm coupling anddriven about the elbow axis of rotation by the second rotary drive. Asubstrate support is supporting the substrate, the substrate supportrotatably coupled to the forearm and rotatable about a wrist axis ofrotation of the forearm, the wrist axis of rotation offset from theelbow axis of rotation by a forearm link length. The substrate supportis further coupled to the upper arm with a substrate support couplingand driven about the wrist axis of rotation by relative movement betweenthe forearm and the upper arm about the elbow axis of rotation. Theforearm link length is different than the upper arm link length. Thesubstrate support is constrained by the substrate support coupling suchthat the substrate moves along a linear path with respect to the centralaxis of rotation.

In accordance with another aspect of the exemplary embodiment, thelinear path is along a direction that intersects the central axis ofrotation.

In accordance with another aspect of the exemplary embodiment, thelinear path is along a direction that is perpendicular to and offsetwith respect to the central axis of rotation.

In accordance with another aspect of the exemplary embodiment, the wristaxis of rotation moves along wrist path parallel to the linear path.

In accordance with another aspect of the exemplary embodiment, thesubstrate support coupling comprises a band drive having one or more noncircular pulleys.

In accordance with another aspect of the exemplary embodiment, theforearm coupling comprises a band drive having one or more non circularpulleys.

In accordance with another aspect of the exemplary embodiment, atransport apparatus has a drive; a first arm connected to the drive,where the first arm comprises a first link, a second link and an endeffector connected in series with the drive, where the first link andthe second link have different effective lengths; and a system forlimiting rotation of the end effector relative to the second link toprovide substantially only straight movement of the end effectorrelative to the drive when the first arm is extended or retracted.

In accordance with another aspect of the exemplary embodiment, theeffective length of the first link is shorter than the effective lengthof the second link.

In accordance with another aspect of the exemplary embodiment, theeffective length of the first link is longer than the effective lengthof the second link.

In accordance with another aspect of the exemplary embodiment, the endeffector comprises a lateral offset between a wrist joint with thesecond link and a centerline of a substrate support section which isabout equal to a difference in the effective lengths of the first andsecond links.

In accordance with another aspect of the exemplary embodiment, thesystem for limiting rotation is configured to translate the end effectorwhen the first arm is extended or retracted with the wrist joint beingmaintained at the lateral offset relative to a center axis of rotationof the drive.

In accordance with another aspect of the exemplary embodiment, thesystem for limiting rotation of the end effector provides substantiallyonly radial movement of the end effector relative to the drive when thefirst arm is extended or retracted.

In accordance with another aspect of the exemplary embodiment, thesystem for limiting rotation of the end effector is configured toconstrain orientation of the end effector such that the end effectorpoints radially relative to the drive regardless of positions of thefirst and second links.

In accordance with another aspect of the exemplary embodiment, the endeffector is configured to support at least two spaced substratesthereon, and where a lateral offset is provided between a wrist joint ofthe end effector with the second link and a center of a path of straightlinear movement of the end effector, when the first arm is extended orretracted, for substantially translation only movement of the endeffector when the first arm is extended or retracted with the wristjoint being maintained at the lateral offset relative to a center axisof rotation of the drive.

In accordance with another aspect of the exemplary embodiment, thesystem for limiting rotation comprises a band drive comprising pulleysand a band.

In accordance with another aspect of the exemplary embodiment, thepulleys comprise at least one non-circular pulley.

In accordance with another aspect of the exemplary embodiment, thepulleys comprise at least one pulley stationarily connected to thesecond link or the end effector.

In accordance with another aspect of the exemplary embodiment, the endeffector comprises a substrate support section and a leg connecting thesubstrate support section to a wrist joint of the end effector with thesecond link, where the leg has a first section connected to the wristjoint, a second section connected to the substrate support section, andwhere the first and second sections are connected to each other at anangle of between about 90 degrees and about 120 degrees.

In accordance with another aspect of the exemplary embodiment, the endeffector comprises two substrate support sections and a leg frameconnecting the substrate support section to a wrist joint of the endeffector with the second link, where the leg frame is substantiallyU-shaped with a base and two legs, where each leg is connected to aseparate one of the substrate support sections, and where the wristjoint connects the end effector to the second link at a location offsetfrom a center of the base.

In accordance with another aspect of the exemplary embodiment, a methodis provided comprising: rotating a first link of an arm by a drive;rotating a second link of the arm when the first link is rotated, wherethe second link is rotated on the first link; and rotating an endeffector on the second link, where the first and second links havedifferent effective lengths, and where rotation of the end effector onthe second link is constrained such that, when the arm is extended orretracted, the end effector is limited to substantially only straightmovement relative to the drive.

In accordance with another aspect of the exemplary embodiment, themovement is radial movement relative to a center axis of the drive.

In accordance with another aspect of the exemplary embodiment, the endeffector comprises a lateral offset between a wrist joint with thesecond link and a centerline of a substrate support section which isabout equal to a difference in the effective lengths of the first andsecond links.

In accordance with another aspect of the exemplary embodiment, rotatingthe end effector on the second link results in translation motion onlyof the end effector when the first arm is extended or retracted with awrist joint with the second link being maintained at a lateral offsetrelative to a center axis of rotation of the drive.

In accordance with another aspect of the exemplary embodiment, rotatingthe end effector provides substantially only radial movement of the endeffector relative to the drive when the first arm is extended orretracted.

In accordance with another aspect of the exemplary embodiment, rotatingthe end effector constrains orientation of the end effector such thatthe end effector points radially relative to the drive regardless ofpositions of the first and second links.

In accordance with another aspect of the exemplary embodiment, atransport apparatus is provided having a drive; and an arm connected tothe drive, where the arm comprises a first link connected to the driveat a first joint, a second link connected to the first link at a secondjoint, and an end effector connected to the second link at a thirdjoint, where the first link comprises a first length between the firstand second joints which is different from a second length of the secondlink between the second and third joints, where movement of the endeffector at the third joint is constrained to track in a substantiallystraight radial line relative to the center of rotation of the driveduring extending and retracting of the arm.

In accordance with one example embodiment, a transport apparatuscomprises a drive; a first arm connected to the drive, where the firstarm comprises a first link, a second link and an end effector connectedin series with the drive, where the first link and the second link havedifferent effective lengths; and a system for limiting rotation of theend effector relative to the second link to provide substantially onlystraight movement of the end effector relative to the drive when thefirst arm is extended or retracted.

The effective length of the first link may be shorter than the effectivelength of the second link. The effective length of the first link may belonger than the effective length of the second link. The end effectormay comprise a lateral offset between a wrist joint with the second linkand a centerline of a substrate support section which is about equal toa difference in the effective lengths of the first and second links. Thesystem for limiting rotation may be configured to translate the endeffector when the first arm is extended or retracted with the wristjoint being maintained at the lateral offset relative to a center axisof rotation of the drive. The system for limiting rotation of the endeffector may provide substantially only radial movement of the endeffector relative to the drive when the first arm is extended orretracted. The system for limiting rotation of the end effector may beconfigured to constrain orientation of the end effector such that theend effector points radially relative to the drive regardless ofpositions of the first and second links. The end effector may beconfigured to support at least two spaced substrates thereon, and wherea lateral offset is provided between a wrist joint of the end effectorwith the second link and a center of a path of straight linear movementof the end effector, when the first arm is extended or retracted, forsubstantially translation only movement of the end effector when thefirst arm is extended or retracted with the wrist joint being maintainedat the lateral offset relative to a center axis of rotation of thedrive. The system for limiting rotation may comprise a band drivecomprising pulleys and a band. The pulleys may comprise at least onenon-circular pulley. The pulleys may comprise at least one pulleystationarily connected to the second link or the end effector. The endeffector may comprise a substrate support section and a leg connectingthe substrate support section to a wrist joint of the end effector withthe second link, where the leg has a first section connected to thewrist joint, a second section connected to the substrate supportsection, and where the first and second sections are connected to eachother at an angle of between about 90 degrees and about 120 degrees. Theend effector may comprise two substrate support sections and a leg frameconnecting the substrate support section to a wrist joint of the endeffector with the second link, where the leg frame is substantiallyU-shaped with a base and two legs, where each leg is connected to aseparate one of the substrate support sections, and where the wristjoint connects the end effector to the second link at a location offsetfrom a center of the base.

One type of example method may comprise rotating a first link of an armby a drive; rotating a second link of the arm when the first link isrotated, where the second link is rotated on the first link; androtating an end effector on the second link, where the first and secondlinks have different effective lengths, and where rotation of the endeffector on the second link is constrained such that, when the arm isextended or retracted, the end effector is limited to substantially onlystraight movement relative to the drive.

The movement may be radial movement relative to a center axis of thedrive. The end effector may comprise a lateral offset between a wristjoint with the second link and a centerline of a substrate supportsection which is about equal to a difference in the effective lengths ofthe first and second links. Rotating the end effector on the second linkmay result in translation motion only of the end effector when the firstarm is extended or retracted with a wrist joint with the second linkbeing maintained at a lateral offset relative to a center axis ofrotation of the drive. The end effector may provide substantially onlyradial movement of the end effector relative to the drive when the firstarm is extended or retracted. Rotating the end effector may constrainorientation of the end effector such that the end effector pointsradially relative to the drive regardless of positions of the first andsecond links.

One type of example embodiment may be provided in a transport apparatuscomprising a drive; and an arm connected to the drive, where the armcomprises a first link connected to the drive at a first joint, a secondlink connected to the first link at a second joint, and an end effectorconnected to the second link at a third joint, where the first linkcomprises a first length between the first and second joints which isdifferent from a second length of the second link between the second andthird joints, where movement of the end effector at the third joint isconstrained to track in a substantially straight radial line relative tothe center of rotation of the drive during extending and retracting ofthe arm.

Referring now to FIG. 63, there is shown a graphical representation 1100of exemplary pulleys. The exemplary pulley profiles may be for an armwith unequal link lengths as will be described. By way of example, thegraph 1100 may show profiles for a wrist pulley where the elbow pulleyis circular. Here, the following example design was used for the figure:Re/l2=0.2 where Re is the radius of the elbow pulley and l2 is thejoint-to-joint length of the forearm. Alternately, any suitable ratiomay be provided. For the purpose of clarity, the graph shows extremedesign cases in comparison with a pulley for an equal-link arm. The mostouter profile 1110 is for l2/l1=2, where l2 is the joint-to-joint lengthof the forearm and l1 is the joint-to-joint length of the upper arm, forexample, this case represents a longer forearm. The middle profile 1112is for l2/l1=1, for example, a case with equal link lengths. The mostinner profile 1114 is for l2/l1=0.5, for example, this case represents ashorter forearm. In the embodiment shown, a polar coordinate system 1120is used. Here, the radial distance is normalized with respect to theradius of the elbow pulley, for example, expressed as a multiple of theradius of the elbow pulley. In other words, Rw/Re is shown, where Rwrepresents polar coordinates of the wrist pulley with Re representingthe elbow pulley. The angular coordinates are in deg, and the zeropoints along the direction 1122 of the end-effector, for example, theend-effector points to the right with respect to the figure.

Referring now to FIGS. 64 and 65, there is shown two additionalconfigurations of the arm with unequal link lengths 1140 and 1150. Arm1140 is shown with a forearm 1144 longer than upper arm 1142 where thesingle arm configuration may utilize the features as disclosed withrespect to FIGS. 1-4 and 5-8 or otherwise. In the embodiment shown, twoend-effectors 1146, 1148 supporting respective substrates 1150, 1152 areconnected rigidly to each other and pointing in opposing directions. Thesubstrates travel in a radial path that coincides with the center 1156of robot 1140 and offset 1154 from the wrist as shown. Similarly, arm1160 is shown with a forearm 1164 shorter than upper arm 1162 where thesingle arm configuration may utilize the features as disclosed withrespect to FIGS. 1-4 and 5-8 or otherwise. In the embodiment shown, twoend-effectors 1166, 1168 supporting respective substrates 1170, 1172 areconnected rigidly to each other and pointing in opposing directions. Thesubstrates travel in a radial path that coincides with the center 1176of robot 1160 and offset 1174 from the wrist as shown. Here, thefeatures of the disclosed embodiments may be similarly shared with anyof the other disclosed embodiments.

It should be seen that the foregoing description is only illustrative.Various alternatives and modifications can be devised by those skilledin the art. Accordingly, the present embodiment is intended to embraceall such alternatives, modifications, and variances. For example,features recited in the various dependent claims could be combined witheach other in any suitable combination(s). In addition, features fromdifferent embodiments described above could be selectively combined intoa new embodiment. Accordingly, the description is intended to embraceall such alternatives, modifications and variances which fall within thescope of the appended claims.

1. A transport apparatus comprising: a drive; a first arm connected tothe drive, where the first arm comprises a first link, a second link andan end effector connected in series with the drive, where the first linkand the second link have different effective lengths; and a system forlimiting rotation of the end effector relative to the second link toprovide substantially only straight movement of the end effectorrelative to the drive when the first arm is extended or retracted.
 2. Atransport apparatus as in claim 1 where the effective length of thefirst link is shorter than the effective length of the second link.
 3. Atransport apparatus as in claim 1 where the effective length of thefirst link is longer than the effective length of the second link.
 4. Atransport apparatus as in claim 1 where the end effector comprises alateral offset between a wrist joint with the second link and acenterline of a substrate support section which is about equal to adifference in the effective lengths of the first and second links.
 5. Atransport apparatus as in claim 4 where the system for limiting rotationis configured to translate the end effector when the first arm isextended or retracted with the wrist joint being maintained at thelateral offset relative to a center axis of rotation of the drive.
 6. Atransport apparatus as in claim 1 where the system for limiting rotationof the end effector provides substantially only radial movement of theend effector relative to the drive when the first arm is extended orretracted.
 7. A transport apparatus as in claim 1 where the system forlimiting rotation of the end effector is configured to constrainorientation of the end effector such that the end effector pointsradially relative to the drive regardless of positions of the first andsecond links.
 8. A transport apparatus as in claim 1 where the endeffector is configured to support at least two spaced substratesthereon, and where a lateral offset is provided between a wrist joint ofthe end effector with the second link and a center of a path of straightlinear movement of the end effector, when the first arm is extended orretracted, for substantially translation only movement of the endeffector when the first arm is extended or retracted with the wristjoint being maintained at the lateral offset relative to a center axisof rotation of the drive.
 9. A transport apparatus as in claim 1 wherethe system for limiting rotation comprises a band drive comprisingpulleys and a band.
 10. A transport apparatus as in claim 9 where thepulleys comprise at least one non-circular pulley.
 11. A transportapparatus as in claim 9 where the pulleys comprise at least one pulleystationarily connected to the second link or the end effector.
 12. Atransport apparatus as in claim 1 where the end effector comprises asubstrate support section and a leg connecting the substrate supportsection to a wrist joint of the end effector with the second link, wherethe leg has a first section connected to the wrist joint, a secondsection connected to the substrate support section, and where the firstand second sections are connected to each other at an angle of betweenabout 90 degrees and about 120 degrees.
 13. A transport apparatus as inclaim 1 where the end effector comprises two substrate support sectionsand a leg frame connecting the substrate support section to a wristjoint of the end effector with the second link, where the leg frame issubstantially U-shaped with a base and two legs, where each leg isconnected to a separate one of the substrate support sections, and wherethe wrist joint connects the end effector to the second link at alocation offset from a center of the base.
 14. A method comprising:rotating a first link of an arm by a drive; rotating a second link ofthe arm when the first link is rotated, where the second link is rotatedon the first link; and rotating an end effector on the second link,where the first and second links have different effective lengths, andwhere rotation of the end effector on the second link is constrainedsuch that, when the arm is extended or retracted, the end effector islimited to substantially only straight movement relative to the drive.15. A method as in claim 14 where the movement is radial movementrelative to a center axis of the drive.
 16. A method as in claim 14where the end effector comprises a lateral offset between a wrist jointwith the second link and a centerline of a substrate support sectionwhich is about equal to a difference in the effective lengths of thefirst and second links.
 17. A method as in claim 14 where rotating theend effector on the second link results in translation motion only ofthe end effector when the first arm is extended or retracted with awrist joint with the second link being maintained at a lateral offsetrelative to a center axis of rotation of the drive.
 18. A method as inclaim 14 where rotating the end effector provides substantially onlyradial movement of the end effector relative to the drive when the firstarm is extended or refracted.
 19. A method as in claim 14 where rotatingthe end effector constrains orientation of the end effector such thatthe end effector points radially relative to the drive regardless ofpositions of the first and second links.
 20. A transport apparatuscomprising: a drive; and an arm connected to the drive, where the armcomprises a first link connected to the drive at a first joint, a secondlink connected to the first link at a second joint, and an end effectorconnected to the second link at a third joint, where the first linkcomprises a first length between the first and second joints which isdifferent from a second length of the second link between the second andthird joints, where movement of the end effector at the third joint isconstrained to track in a substantially straight radial line relative tothe center of rotation of the drive during extending and retracting ofthe arm.